When you multiply ingredients like this, you need to adjust the recipe. It is not a simple multiplication. Suggest looking at food service recipe books for guidance.
28 cups is 7 quarts, plus you need clearance for the mixing, so you'll need something with a 10ish quart bowl. I think the only thing that would fit the bill is a commercial mixer. Even a small (i.e. 12-quart) Hobart will set you back over $4000. I wouldn't necessarily be worried about doubling the recipe - the Cake Bible has scalable cake recipes, and the leavening changes are based on the size of the pans you're baking them in, so if you're baking them in the same size pans the recipe was written for it should work. I vote you mix the batter twice unless you are doing a serious amount of baking, a commercial mixer would not be a great investment!
Have you doubled this recipe before? I think it can be tricky. My own choice would be to make the recipe twice. You can do the prep for both at once, but mix separately or make the second while the first bakes.
You'd need a big one - maybe a Hobart?
But bear in mind that it might not work the same if you just double quantities - raising agents in particular don't work the same if you just double the amounts. You're probably better off doing it in two batches.
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But bear in mind that it might not work the same if you just double quantities - raising agents in particular don't work the same if you just double the amounts. You're probably better off doing it in two batches.