Here is the info from the DLR website:
Order a Disneyland Resort Personal-Size Party Cake
Celebrate your birthday with a meal at a full-service restaurant in Disneyland Park, Disney California Adventure Park or the Disneyland Resort Hotels, and add to the fun with a Disney Princess Jewelry Box or Disney Pirate Treasure Chest! Each comes with a special surprise and an individual cake! The Princess Jewelry Box and the Disney Pirate Treasure Chest are available at full-service restaurants, Character dining locations, and through Disney Hotel Room Service.
Price: $15 each, plus tax.
Are you staying at an onsite hotel? If so, you could do an In Room Celebration as well, but they are limited to what they do in the restaurants.
On a side note, I have not heard good reviews regarding the treasure chest cakes. I hear they look nice, but taste terrible.