You can find GF cake mixes in most grocery stores. Quality varies. You can usually make a good GF cake using a GF replacement flour (make sure to include xanthan gum for texture), but the quality of the flour and the taste of the replacements are pretty individual. There are good blogs with GF cake recipes if you care to research.
OR you can go in a completely different direction and make a cheesecake, or GF brownies (which have very little flour so no worries about texture or taste), or pudding, or mousse....think about flourless chocolate cake, for example, which is not a typical birthday cake but is super yummy.