The FDA says that
So both your cake and hers can legally be labeled “chocolate cake.”
Eggs! Eggs are in chocolate cake. And milk! Oh, goody! And wheat! That’s nutrition!
You’ll have to leave now.
Is this a hypothetical?
Let me tell you about the time my fury burned with the heat of a 100 watt incandescent lightbulb…
I was but a bachelor, doing my grocery shopping (which actually consisted of lunch and dinner ingredients, not just frozen meals) when I happened upon the bakery section and noticed a pink-frosted layer cake labelled as “Cherry.” I bought it, took it home and proceeded to cut into it only to find that the cake inside was a simple white cake with no cherry flavoring at all. In fact, the frosting wasn’t even particularly cherry flavored, it was just pink.
It tasted like crap. I only wish I had had Skald around to exact some sweet revenge on the purveyor of such a fraud. I had to settle for increasingly high-pitched ranting to friends, family, and anyone else who would listen which is why I now resort to the SDMB for all of my social interaction.
Because I obviously couldn’t have a sister, a wife, or enjoy baking for the hell of it?
Get a grip, dude.
This, in addition to my general anal-retentiveness and my diabetes and the need to control the ingredients, is why I prefer to do my own baking. My sister (who is a good cook, don’t misunderstand me) only gets away with never making desserts because I love her. 
Can I have a lemonade?
Maybe you shouldn’t have started all those hypothetical polls. 
That escalated quickly.
Are you posting from some strange alternate universe in which I am not perpetually grumpy?
I have to say, I shudder to think what horrible pastries you’ve been eating all your life if you refer to cake as “the bread part”.
Did you miss the part of the OP where the cake I was making for myself and the missus lacked icing completely?
Anyway, I used that expression because saying “the cake part” and “the icing” would be leadng the witness. Anyway, icing-less cake IS a form of bread. Now get you to a bakery before I give my 2789-word lecture on why beer is ALSO bread. 
Cake has a flavor. Cake is also often (but not always) topped by some sort of icing. Icing also has a flavor. The icing on a cake may or may not have the same flavor as the cake.
And to refer to a cake as an <adjective> cake is usually to imply that the cake has <adjective> flavoring. A chocolate cake, thus, would be expected to have chocolate flavoring. Cocoa is the portion of chocolate which gives it its flavor, and thus a chocolate cake contains chocolate flavoring, that is to say, cocoa. It may or may not also contain the other portion of chocolate, chocolate butter, which mostly contributes texture to chocolate, but the texture of cake is very different from the texture of chocolate, and so is not used adjectivally to describe a cake.
Yes.
Seriously, what is wrong with you people? Where are my damn recipes?
You’ll pay for this. You, and then one day, your heirs!
A bit surprised that it got this far without someone pointing out that the icing on a cake is just the icing on the cake.