Do you have the Dine Out GP? If so, I believe you can get a birthday cake at a restaurant, click on your Sims table and there should be an option to request one. I've never tried it myself, but I've read threads on here of other Simmers who have gotten one that way.
Other than that, the only other way I can think to get one would be to buy one at a Bakery if you have one in your world and the Get to Work EP.
EDIT: Just thought of one more way. Throw a birthday party at another location and hire a caterer. They are supposed to bake a birthday cake for the party. Some Simmers haven't had much luck with that though. You could always bake one yourself there too I suppose. Just make sure there's a stove on the venue lot. :)
