Unsurprisingly, there are lots of bits of furniture around that are based on the Rubik's cube; coffee tables are particularly popular, and for 980€ (!!), you can even buy a Rubik's cube locker. I wanted to do something different, and use lazy Susan bearings to achieve at least one axis of rotation - they're cheap, really strong, and add a wacky dimension to a chest of drawers.
The design is simply three boxes, each containing a single drawer. Their construction is basic - they're made of 1/4" and 1/2" plywood (which you should get precut at the lumber yard into two 2'x8' sheets), and assembled using a brad nailer and wood glue. This method of construction is super fast and precise, and results in really strong objects. The main challenge in this build is cutting the pieces with high precision - if you can't cut plywood to within 1 mm, you should probably practice on something simpler until you can. Having said that, I'm no pro and I've never made a chest of drawers before, so this project is NOT fancy woodworking by any means! If you weren't fussed about the drawers, it would be dead easy - it's just three boxes and a couple of lazy Susans, and you'd have a cool coffee table with no additionally functionality aside from rotatability. Deluxe Scrabble, anyone?
I was going to simply glue the "stickers" on to decorate the outside - or even just paint them on - but the future owner insisted he had to be able to scramble and "solve" the cube, so I enabled this with the help of rare-earth magnets for holding power and short dowels for positioning. I'm glad I did - it's more fun now, and the colors can be selected to match your mood or decor, including impossible combos of color (insofar as the real cube goes).
The puzzle is a little under 60 mm across, and this chest of drawers is exactly 600 mm across, so it is in approximately 10:1 scale. 1000 regular Rubik's cubes would therefore fit inside.
There are cubes that are 2x2, 4x4, 5x5 etc, so if you need more (or less) drawers, there is an obvious design solution...