Yes, I believe his birthdate was mentioned in the episode when he dreams about getting his boater's license.

However, I still believe his age is left purposely ambiguous. His behavior is full of contradictions. For example, he is mature and independent enough to live on his own and hold a job but he still engages in very childish mannerisms. However, it is fair to say that I think he is the youngest of the main characters on the show. Patrick and Sandy are probably around his age bracket, early to mid-twenties. I see Squidward as being slightly older, maybe later twenties to early thirties. And Mr. Krabs and Plankton being middle-aged.