The mathematical name for these is Hexahedrons. For legal reasons I cannot provide you with a Hexahedron of size 3.

A size 5 Box is similar to the Professor Cube™, available from Uwe Mèffert. An image of the puzzle.
A plastic puzzle similar to this was once manufactured. An image of the puzzle.
A size 6 Box has never been made in physical form, as far as I know. An image of the puzzle.
This 11*11 box may hold the record for the largest 'twisty box' puzzle that has ever been put on a computer. If you know of a larger one, please show me it. An image of the puzzle.