The video was posted about about a week before the Nov. 21 release of The Imitation Game, which sees Cumberbatch playing English mathematician Alan Turing, whose brilliant mind helped crack the Enigma code during World War II.
Cumberbatch has demonstrated celebrity impressions before. He has mimicked Rickman several times, including on The Jonathan Ross Show in his native England and on TheTonight Show Starring Jimmy Fallon, during which he and host Jimmy Fallon (naturally) engaged in an "Alan Rickman-off." Cumberbatch promptly Severus Snape-d part Snoop Dogg's popular 1994 track "Gin and Juice" and Sir Mix A Lot's 1992 one hit wonder "Baby Got Back."
On the former series last year, the British star also did his impersonation of David Tennant, who stars in the new series Gracepoint and used to play the title role in the BBC's cult sci-fi series Doctor Who, as well as of the host Jonathon Ross, who pronounces his R's as W's, which has earned him the nickname "Wossy."
Also last year, on the BBC series The Graham Norton Show, Cumberbatch did his best Chewbacca in front of Star Wars veteran Harrison Ford (whose reaction was priceless).
He appeared on the show again this past October and did an impression of another Star Wars character whose popularity level is probably negative 12 times infinity.