The day I received it in the mail I spent quite a bit of time solving it. The problem is it is extremely difficult to visualise and retain the solution in your head. Some other puzzles I find easy to visualise, but this is very hard to see with my mind's eye for some reason. The first day that I put it together I logically solved what position in the cube each block is constrained to, and drew this pic as that proof.

This was not enough though, as it still took some time reassembling the cube after unravelling it to show children and other visitors. I inevitably had to put it together again every damn time. I decided that a simpler solution was needed, so after reassembling it today I drew a digram showing how the blocks were linked. Then I sat down and created the following wrl that lets you see how it is linked together.
I no longer need be reluctant to show the puzzle to people because now I can reassemble it in seconds. Woo hoo!!
The wrl was surprisingly simple to create. It is only 7k uncompressed. Thank heavens for PROTOs!