Something that looks likes this (preferably with the gold insert): (sorry it wouldn't let me attach it)
What is the typical size? 4x4x4?
these are the cupcake boxes I ordered on etsy. they might fit your mini cakes.
Try googling it.... dang! I bought some of these and now I am having a brain-freeze as to where I got them! CK PRoducts, Nashville Wraps, TheBoxDepot, efavormart, papermart.com......... that's all I can think of right now.
Try this link
Looks almost the same
I got some at papermart.com