Do hedgehogs also store things in their cheeks like hamsters?
No they don't, but they are voracious little buggers, they don't eat as much as they make food disappear. At least the one I was taking care of would vacuum food until satisfied. Here's an example: http://youtu.be/7IKYU9Kbego (I was raising a wild one for release)
Edit: Oh, and they like to chew random things. They do this to mask their smell. They chew and lick these random things and then lick themselves. The end result is a certain amount of random destruction and gnawed items.