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These are puppet shows rather than CGI cartoons, but could you be thinking of Johnson and Friends or The Secret Life of Toys?
There aren't many CGI cartoons that were released in 2002 or earlier (going by this list [1]
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Make Way for Noddy from 2002 had an elephant character, but a lot of the characters aren’t animals so it probably isn’t it.
Edited by mlaThe Make Way For Noddy comment actually reminded me of something that could be the show you are thinking of. There's an episode of The Noddy Shop (aired on PBS from 1998-2000 and reran until 2002) called "Take A Stand" that has a song called "Warlo's Cake" (which sounds like "we love cake") in it, but that's live-action with puppets and the only animals in that show are a robot dog, two pigs, an alligator, some penguins and a crawfish. That episode isn't online but is mentioned on the Wikipedia article for the show. The Noddy segments that played during the episodes were stop-motion, which looks CGI. Could that have been it?
Edited by mimitchi33

So i just remembered this one cartoon i used to watch a lot on VHS when i was 4. The remember it being in Cgi with this cast of animal characters(i think one of them was a horse?).
I vaguely remember one of the episodes involving a character’s birthday Towards the end, there were elephants who sang “We love cake”
If i had to guess, it would probably be from between 1995-2002
I don’t really know anything else about this show as it wasn’t on any cable networks i knew of
Edited by MintyStarryNights