Cakehole is a rude, joking British word for someone’s mouth. You hear it most when one person is telling another to be quiet: “Shut your cakehole.” It is not for class, not for emails, and not for anyone you need to show respect to. It is comic and rough on purpose, as if the mouth were just a hole you push cake into. American English is more likely to say shut your mouth or shut your trap. Even in Britain, many people would never use cakehole; it belongs to sharp, informal speech, and it can sound unkind if the room is not already joking.