This is a project we just finished in my engineering class. Basically we started out by making multiple sketches, then built the cube in inventor, and lastly put it together by glueing wooden cubes together. It took a little bit of sanding to make the pieces fit just right, but in the end it turned out great. I also chose to paint mine and I'm sorry I know it is very cheap paint I didn't have time to get any better. This is a very fun and easy project to make especially for kids. You can design it yourself and make any size or difficulty. Have fun solving!
(Also sorry about the chips and smudges in the paint I haven't gone back to fix it yet)