Amy and Rory wake up one morning to find that the entire Earth is overrun with little black cubes. The Doctor is already investigating, suspicious that an alien invasion is in progress, but the cubes are featureless and inert. Even the assistance of both Brian Williams and Kate Stewart -- UNIT's head of scientific research and the daughter of the Doctor's old friend, the Brigadier -- brings him no closer to solving the mystery. As the Doctor's stay in their home stretches into weeks and then months, Amy and Rory are forced to confront their own future as adventurers in time and space. And then, one day, the cubes activate...

It was always intended that Chris Chibnall would write two scripts for Doctor Who's thirty-third season. From an early stage he was scheduled to write episode two, Dinosaurs On A Spaceship, which was planned to be one of four installments to air in the autumn of 2012. This portion of Season Thirty-Three would culminate in the departure of Amy and Rory, after which a new companion would be introduced in the subsequent Christmas special. Chibnall was then expected to contribute a second adventure which would feature the new series regular, and be included amongst nine episodes broadcast in Spring 2013.

Around December 2011, however, it was decided to rebalance the two segments of Season Thirty-Three by bringing an additional episode forward to the fall. Executive producer Steven Moffat wanted to explore Amy and Rory's life from their perspective, with the Doctor haphazardly appearing to take them on occasional adventures. Having been pleased with Chibnall's portrayal of their relationship in the early drafts of Dinosaurs On A Spaceship, Moffat offered him this additional script on top of the story which would feature the new companion. Chibnall agreed, and he began developing the narrative -- which would form Amy and Rory's penultimate appearance -- around the end of January 2012. Rory's father, Mark, was given a prominent role in the new storyline; he had been a popular element of the script for Dinosaurs On A Spaceship. Meanwhile, Chibnall learned that his mystery-drama series Broadchurch was being commissioned by ITV. As a result, while he would still be able to complete the Amy-Rory adventure, he would now be unable to write his planned third script for the season.

The basic premise for the episode was to follow Amy and Rory over the course of a year

Moffat's basic premise for the episode was to follow Amy and Rory over the course of a year, punctuated by the Doctor's visits. Looking for a plot which would sustain such a timeframe, Chibnall thought in terms of a methodical invasion of Earth. This drew upon his childhood love for the Jon Pertwee era, in which the Third Doctor regularly defended the planet from extraterrestrial incursions. In turn, this suggested the involvement of the Unified Intelligence Taskforce (UNIT), which had been prominent in many Pertwee stories under the leadership of Brigadier Alistair Lethbridge-Stewart, as played by Nicholas Courtney. Indeed, the Doctor had served as UNIT's scientific adviser during a lengthy period of time in which he was exiled to Earth.

Since the return of Doctor Who in 2005, UNIT had taken a largely peripheral role, with the exception of a handful of adventures such as Season Thirty's The Sontaran Stratagem / The Poison Sky and the 2009 Easter special, Planet Of The Dead. With Courtney having passed away in February 2011, Chibnall was keen to pay him tribute by introducing the Brigadier's daughter, Kate, as the new leader of UNIT. As a twist, Kate Stewart would not be a soldier like her father, but rather the head of scientific research. Effectively, then, she would inherit the roles of both the Brigadier and the Doctor within UNIT. Coincidentally, Doctor Who spin-off media had already introduced a daughter named Kate for the Brigadier -- created by Marc Platt for the 1995 Reeltime Pictures video drama Downtime -- but Chibnall had no knowledge of this character.

For the manner of his story's slow invasion, Chibnall was inspired by a 2007 shipwreck along the Devon coast near his home, when people showed up in droves to claim cargo which had washed up on the shore. This led to the notion of the general public collecting alien items which initially appeared to be innocuous, but which would ultimately be revealed to have a more sinister purpose. These objects inspired the story's working title, “Cubed”, which also served as a mathematical allusion to the strength of the Doctor-Amy-Rory team.

One major element of Chibnall's early drafts which was eventually dropped involved the appearance of Prime Minister Stephen Carter. Suspicious of the Doctor, Carter would bar him from the United Kingdom, resulting in the Time Lord's absence from a long stretch of the narrative. At the story's conclusion, Brian was initially uneasy when Amy and Rory decided to take “one more trip” in the TARDIS. Moffat suggested that Brian should instead encourage his son and daughter-in-law to go with the Doctor, providing a less sombre and more subtle lead-in to their final story, The Angels Take Manhattan.

Cast as Kate Stewart was Jemma Redgrave, scion of the Redgrave family of actors

“Cubed” was made on its own as Season Thirty-Three's third production block. The director was Douglas Mackinnon, who had previously handled The Sontaran Stratagem / The Poison Sky; in the interim, he had also made two Doctor Who mini-episodes which appeared on the DVD release for Season Thirty-Two under the banner Night And The Doctor. Cast as Kate Stewart was Jemma Redgrave, scion of the Redgrave family of actors which included her father Corin, her aunts Lynn and Vanessa, her grandfather Michael, and her great-grandfather Roy. She was an accomplished performer in her own right, having starred in television programmes like Bramwell and Fish alongside appearances in movies such as Howards End.

Filming for “Cubed” began on April 30th in Penarth; the engagement party was held at the Villa Napoli Restaurant, while the interior of Amy and Rory's home was again a residence on Church Road. Work at the latter location continued on May 1st, with Redgrave joining the cast. On the 2nd and 3rd, Mackinnon's team moved to Caerphilly Castle in Caerphilly. It principally served as UNIT headquarters beneath the Tower of London, although the material in Henry VIII's bedroom was also taped there on the first day, and the Doctor and Amy's rooftop conversation was shot against a green screen on the second day. Recording on May 4th began at Coedarhydyglyn, a private house in St Nicholas, for the material in 1890 France as well as Brian's study. Cast and crew then relocated to Bute Esplanade in Cardiff Bay, where another private dwelling was again pressed into service as the exterior of Amy and Rory's home. On May 5th, Rory's workplace was actually St Cadoc's Hospital in Caerleon. Also recorded there was an ultimately-unused side adventure for the TARDIS crew, in which Amy and Rory defused a bomb which threatened an alien convoy.

After a day off on Sunday the 6th, it was back to Church Road on May 7th and 8th, with the back garden now joining the interior on camera. On the 9th, material in the UNIT laboratory was recorded at Neath Abbey in Neath, as was Brian's video footage of his cube. The sequences in the Shakri Sanctum were then taped at Doctor Who's regular studio facilities in Upper Boat on May 10th and 11th; the set for Amy and Rory's kitchen was also in use on the first day, as was the standing TARDIS set on the second day. This marked the show's final work at Upper Boat after being housed there for almost six years, since the transition to the BBC's new Roath Lock Studios complex in Cardiff was effectively complete.

May 12th, in turn, was intended to bring Karen Gillan and Arthur Darvill's time on Doctor Who to a close. The venue was again St Cadoc's, although in addition to the remaining hospital footage, Mackinnon wrapped up the day by remounting the final scene of the Doctor, Amy and Rory leaving in the TARDIS. By now, however, it was known that Gillan and Darvill would be appearing as Amy and Rory in the online mini-series Pond Life, which went before the cameras in early June. Simultaneously, Mackinnon was at work on various inserts for “Cubed”; they were captured at the house on Church Road on June 6th, and at Bute Esplanade and near Cardiff's Morgan Arcade on the 7th.

In post-production, however, it was decided to make major changes to Chibnall's episode. In part, this was to introduce the slow invasion storyline earlier: originally, “Cubed” began with scenes such as the adventure with Henry VIII and Amy at the engagement party -- in which she was specifically not asked to be a bridesmaid because she was unreliable and prone to vanish for prolonged periods of time -- but much of the action was resequenced in editing. The other significant cut involved the climax. As recorded, there was an extended action sequence in which Rory took down the two orderlies. Furthermore, the Shakri was physically present, rather than merely appearing as a hologram. He was defeated when Amy and Rory attacked him with the syringes they had retrieved from the orderlies, and the Doctor used his sonic screwdriver on the Shakri's devastating ocular weaponry. However, it was felt that this part of the narrative detracted from the focus on Amy and Rory's life together, and so Chibnall prepared new material to replace it.

As such, a number of new or amended scenes were recorded on June 28th. They included a sequence outside Amy and Rory's house, which was taped at Belle Vue Park in Penarth; more material in their bedroom and back garden, again at Church Road; and additional content aboard the Shakri vessel, against a black cloth at Roath Lock. This, then, became the true end of Gillan and Darvill's tenure on Doctor Who.

Chris Chibnall was eager to feature some celebrity cameos in the episode

But there was still more filming necessary to complete “Cubed”. Chibnall had been eager to feature some celebrity cameos in the episode -- reviving a device occasionally employed on Doctor Who by Moffat's predecessor, Russell T Davies -- and he had suggested appearances by the judges of variety competition Britain's Got Talent or singing contest The Voice UK. Ultimately, it was another reality show, The Apprentice, which agreed to become involved with the episode. On July 29th, a clip was recorded on the boardroom set at The Apprentice's studio in West Acton, London. It saw Karren Brady and Nick Hewer look on as Lord Alan Sugar “fired” the hapless Craig, who was played off-camera by Mackinnon himself. A very different type of celebrity then filmed a segment on July 30th. This was renowned astrophysicist Brian Cox, who stood outside the Holiday Inn Express London-Hammersmith. Finally, in August, the footage of the newsreaders was taped, with contributions from Sophie Raworth of BBC News At One and Matthew Amroliwala of the BBC News Channel.

Meanwhile, by early July, the title “Cubed” had fallen out of favour. Instead, one of Chibnall's new lines of dialogue suggested an alternative: The Power Of Three. Chibnall initially resisted this change, but he eventually came to feel that it was an improvement. For the unique title sequence which accompanied the episode, the Doctor Who logo borrowed the texture of the mysterious cubes. The Power Of Three was broadcast on September 22nd at 7.30pm, five minutes earlier than the two preceding episodes of Doctor Who.

• Doctor Who Magazine Special Edition #33, Spring 2013, “The Power Of Three” by Andrew Pixley, Panini UK Ltd.
• Doctor Who: The Complete History #71, 2015, “Story 229: The Power Of Three”, edited by John Ainsworth, Hachette Partworks Ltd.