Twelve cakes in Chapter 1, two cakes in the rest of the story, none at all after Beorn’s home.  I’ve included the only hyphenated form, seed-cake, here as well as in its own entry as an uncommon word.  It’s milk that makes a dough cakey in my experience.

• 01.022 but he thought a cake or two
• 01.023 just about the time when Bilbo was finishing his second cake
• 01.025 and an extra cake or two,
• 01.029 in fact they had hardly reached the third cake,
• 01.033 He had a horrible thought that the cakes might run short,
• 01.035 But I don’t mind some cake –
• 01.035 seed-cake, if you have any.’
• 01.036 to fetch two beautiful round seed-cakes
• 01.037 and the cake
• 01.046 and all of them for cakes;
• 01.047 the seed-cakes were gone,
• 01.056 And more cakes –
• 03.028 “Mind Bilbo doesn’t eat all the cakes!”
• 07.126 and twice-baked cakes that would keep good a long time,