This is one of those things that never crossed my mind: What would a
tiger do with a box?  Apparently the same thing that a house cat does. 
Oh, and lions and lynx, and other giant felines apparently feel the same
way in this video posted on April 18, 2013 by Big Cat Rescue:

What is up with cats and boxes?  Imagine if people were this way...  Ooooo!  Box!  Then jump into it, roll around and fall asleep.

Actually, I rather like that idea.

More fun animal videos can be found here!