1758, genus name of a type of eight-armed cephalopod mollusks, from Latinized form of Greek oktōpous, literally "eight-foot," from oktō "eight" (see eight) + pous "foot," from PIE root *ped- "foot." Used figuratively since at least 1882 of powers having far-reaching influence (usually as considered harmful and destructive).
The classically correct Greek plural (had the word been used in this sense in ancient Greek) would be octopodes. Octopi (1817) regards the -us in this word as the Latin noun ending that takes -i in plural. Like many modern scientific names of creatures, it was formed in Modern Latin from Greek elements, so it might be allowed to partake of Latin grammar in forming the plural. But since it probably is best to let such words follow the grammar of the language that uses them, and octopuses probably works best in English (unless one wishes also to sanction diplodoci for the dinosaurs).