The First Doctor frees John from the grasp of an octopus by tickling it. (COMIC: Shark Bait)
Octopuses were a species of cephalopods (TV: Terror of the Autons) native to Earth and other planets. According to the First Doctor, there were no pink octopuses anywhere in all the universes. (PROSE: The Plotters)
On Earth[]
Professor Zaroff had a pet octopus. (TV: The Underwater Menace)
Julia Fetch admired octopuses and collected glass sculptures of them. (PROSE: The Drosten's Curse)
Elsewhere[]
On one planet, John was once grabbed by an octopus which restrained him with its tentacles. He was freed by the First Doctor when he tickled it with a feather. (COMIC: Shark Bait)
The Third Doctor compared the Nestenes to cephalopods, specifically octopuses. (TV: Terror of the Autons)
There were methane-breathing octopuses on Neptune in the 32nd century. (PROSE: The Eye of the Tyger)
Keraniums looked similar to octopuses. (AUDIO: "Incubation: Know")