Cake doesn't have a private messaging feature yet. Sorry!
We've discussed adding one and we do have some ideas, but there's lots of other stuff that's taken priority so far.
Private conversations between multiple people (as opposed to private messages between individuals) are a feature that actually existed in an early iteration of Cake, but we removed them because we felt there was too much potential for abuse and misuse. Facebook has been having a lot of trouble with this recently.