My ds1 (nearly 3 yo) longs to be a baby at times and copies the noises my dd (6 mths) makes. Not as bad as your situation but nevertheless annoying.
I think he likes the attention i give to the baby and wants a piece of it!
What i've found helps is i respond really quickly as he's starting to do it by making a really OTT 'babyish' fuss of him...'Ahhhh, are you tired little baby? I think you might need a nap' 'Oh...i forgot you can't talk so poor mummy won't know what you are saying...never mind' etc. He sometimes enjoys playing along for a while, but soon tires of it and wants to be a big boy again.
You have to put on your most patronising voice which helps get rid of some of that inner frustration at the same time!!
They're little monkies, aren't they?