Don't refrigerate the cake. There is enough sugar in the frosting to prevent the formation of any mold.
Linda C

I agree with Linda, but if you want to keep them longer, you can store seven at a time in a large pie keeper. I have two pie keepers, and so I could store 14. You can get the pie keepers at The Container Store, providing they keep them in stock. They seem to run out of them seasonally in November and December.

Lars

Why does everyone say something different. I read some people saying that the sugar prevents it from spoiling and almost all other sites, includin the FDA saying that since it contains milk, it needs to be refrigerated.

I solved the problem and waited until just before I left to make the icing and ice the cupcakes. The leftovers went in the fridge because I didn't want to take any chances.

Everyone gives their personal experience with your question. I think the FDA is based on safety & technically maybe should be refrigerated because of the dairy. I can remember my grandmother leaving food in an unrefrigerated cabinet all day, things the FDA would be screaming about.. Wasn't just her either, I saw it a lot at her friends' homes.
I have not refrigerated cakes with cream cheese frosting for 2 or 3 days & had no problem. Cakes don't tend to last longer that that here. My house is usually on the cool side, I would re-think it if it were very warm.

Tehre are people who think cheese needs refrigeration. It doesn't. It will get more well aged and if there are mold spoors around it will get moldy....but it won't "spoil" in the sense that it will grow bacteria and make you sick.
It's a CYA maneuver....like the wool sweater that says dry clean only.
Do you refrigerate a cake that contains milk? or rolls made with egg yolks? How about a danish with a cream cheese filling? Or those wedding mints made with cream cheese?
If you leave a cream cheese frosting out in a very warm room it may get too soft and sink into the cake....the way a butter cream will do.
By the way....do you refrigerate a buttercream frosted cake? That contains dairy. How about chocolate truffle candy?