We give our bunnies cardboard boxes all the time! They love them! They will definitely chew and tear them up, so it can get messy. Sometimes, the younger rabbits will begin trying to use them as a litter box as well. Just something to consider.
We give plain corrugated cardboard that has no dyes/inks/printed anything on it.
We do pull off any huge clumps of glue and if it all cannot be removed, we don't give that. A little glue, like the type of glue that holds a paper towel tube together, is acceptable for us to give to the buns. We often stuff those tubes with hay and the rabbits use them as toys.
You definitely would want to remove any plastic packing tape -- not sure if the paper-fibre tape is okay or not. I'd probably remove that, too.
Staples are "fine" as long as you monitor that they don't chew at them or they get poked by them, but we usually avoid them.
