With some careful folding of the inflated balloon, you should be able to make it into a very presentable cube.
A fun thing to do with the completed box (balloon) is to disassemble it and draw a scene on the inside surface. so that it’s viewable from the inflating hole when reassembled. If the center square drawing has a bit of depth with the sides, top and bottom relating to the back, you can have an interesting spy-hole presentation
Another thing you could do with the paper ballon is make interesting christmas ornimants. Just let your kids put design to a square sheet of paper; Build the balloon and don’t square it off. Fit your hanger wire into the inflating hole and hang it on the tree! Nice thing about this is storage is a breeze. No broken bulbs!
I challenge someone to build a large enough paper balloon with heavy enough stock to install a computer into it. Should make a great Mod!