If you are staying as a concierge guest at one of the deluxe resorts, the concierge can set this up for you, sometimes a small charge applies, more often it is complimentary.
At deluxe resorts in general, room service should be able to provide this service for a small charge.
At other resorts, I don't believe that they will supply the cake to your room. You would be better off calling the restaurant you will be dining in that evening in advance, and speaking to the manager to make the arrangements for a cake to come to the table. Again, a small fee will likely be applied.
SO NOT wait until you get there, and DO NOT expect that it will happen by mentioning the birthday to the reservationist or front desk person in order to avoid disappointment. If you want the cake, take the initiative in advance to order and be prepared to pay for it on your own.
Have a great trip!
Anne