Yes, look for me and my son we will gladly let you leave a cake, preferably chocolate... Lol! Truly though, you can definitely bring a cake if you rent the space for birthdays and stuff, they have a private area you can also rent. Otherwise, for general attendance they do not like people bringing anything in other then small drinks and snacks.
Your asking if you can bring cake in there? Not 100% sure, I know I've seen cakes go in there, but I'm not sure if there is a birthday package you need to buy or what.
Thanks! Your answer is awaiting moderation.