How many people need to eat it? I'd definitely suggest making several small cakes instead of one large one. You can use one batch of batter but pour it into several small pans instead of a large pan. This way you have a fresh cake for each performance (with complete, frosted edges, not cut edges) and the edges won't go stale quickly. You can bake several at a time, and if you're using them in the same weekend you can stick them in the fridge, but if you need to save them for next week you can freeze it, and then thaw it the day of.
I suspect that actors won't be eating more than a bite or two of the cake, so if for instance you baked your cakes in a 4-inch round, that's a 12.5 inch area, so you could get probably 10-12 "servings" out of a 4-inch cake, plus then it will be GONE which makes it look like "oh wow they ate that whole thing!" (I would recommend pre-cutting the cakes rather than making the actors cut it onstage)
A regular store-bought box of cake mix should make three 4-inch cakes. I don't know how many performances you have, but maybe it's 3 shows per weekend for 2 weeks (just a guess) - I bet you'll be able to find two parents who are willing to each bake one batch of cakes! Baking cake from a box mix is easy and cheap, and I think (if your program is anything like mine was) there are bound to be drama parents who are happy to take on that job.