I have been watching Hazelon AntennaTV and one thing I noticed is Hazel will say:
“Do you want some chocolate cake?”
OK fine, except the cake is yellow and the frosting is dark. You can tell 'cause the cake always has a piece already cut out of it. So I assume the dark frosting is chocolate.
Anyway in your opinion is it proper to call a yellow cake with chocolate frosting, chocolate cake?
Yellow cake always has chocolate frosting (just ask my mother) but yellow cake is yellow cake, unless it is uranium dioxide.
Fortunately for Hazel, my answer would be “yes” either way. 
Chocolate cake is chocolate cake. That is, the cake itself is chocolate. Yellow cake is a basic cake, made with whole eggs, and the egg yolks give the yellow color. White cake is made with egg whites only. Yellow and white cake might have any sort of frosting/icing, or none at all.
If I have my choice, I want yellow cake with either chocolate or strawberry frosting.
If you take away the frosting, how would the cake be identified?
There’s your answer.
It’s cake with chocolate frosting. It isn’t chocolate cake unless the cake itself is chocolaty.
Now I’m hungry for chocolate cake.
No, but they might not have had all our fancy words back then.
My guess is that the reason the slice is already cut and the reason that the cake is yellow are the same: because it shows up well on TV that way. An intact cake would just look like a dark lump on a plate. A chocolate cake with a slice cut out wouldn’t look much different due to lack of contrast between the exterior and the cut portion. But a cake as you describe it is immediately identifiable to the viewer as a cake, even on black & white TV.
So why not just say “cake” in the script? Because “chocolate cake” sounds nicer. Similarly, I’d expect Hazel to offer “chocolate chip cookies” rather than just “cookies.”
All cake is chocolate, all sports cars are red, all mistresses are blond and only the bad guys have mustaches. It’s just the way things are supposed to be.
Magnum, P.I. and Tom Selleck want to have a word with you.
As would Mexico Gibbs.
Usually Hazel offers brownies, which for some reason are the best in the world, along with her coffee. Everyone (even the gangsters on today’s episode) said, "This is THE BEST coffee I ever had.
Now I want Hazel’s brownies and coffee 
I call it chocolate cake.
Chocolate bread covered with chocolate frosting is devil’s food cake.
I knew she was friends with Alice.
I once made the mistake of telling my Mother-in-Law that I didn’t like chocolate cake. I was talking about actual chocolate cake or devil’s food or whatever you want to call it. OTOH, I love yellow cake with chocolate frosting. So she made me a coconut cake for my birthday. I didn’t have the heart to correct her.
But since none of you have gone to the trouble to make me a cake, AND if you think yellow cake is chocolate cake, consider yourself corrected. 
If you offered me chocolate cake and gave me yellow cake, I think I would have to end our friendship - I don’t waste that many calories on yellow cake.
There was actually a thread seven years ago (God, I’m getting old) that asked this question due to Spiderman 2.
You must be my soulmate, Cat Whisperer!
If someone hands me a chocolate cake, I’m expecting chocolate frosting, nice dark chocolate cake, and at least one layer of frosting within the cake.
I remember cupcakes from the school bake sale that were made with yellow cake mix and covered in a layer of chocolate frosting thin enough to be measured in microns. They tasted of disppointment.
What flavour is yellow?
(I don’t eat cake)