Sometimes they are able to bring a cupcake to the birthday person, but not always. If you want something for the entire family to share (they don't bring cupcakes for everyone in the party), or want to be sure that there will be a cake, please call the manager directly in advance (generally they like two days advance notice). They charge a nominal fee for a cake, well worth it to avoid disappointment IMHO.
Don't forget to stop by City Hall on your way in to the MK and pick up a free "birthday" button.
Anne