Pythagorean 3,4,5 = 6 Cube(s) Puzzle

I was told this was impossible to solve. A bit tricky perhaps.

We all know Pythagorus found 3x3 + 4x4 = 5x5 (3,4,5 right angled triangle), but did you know

3x3x3 + 4x4x4 + 5x5x5 = 6x6x6

This puzzle shows this - you can make all three 3x3x3, 4x4x4 and 5x5x5 cubes OR use all the pieces to make a 6x6x6 cube.

I categorised under Toys/Puzzles but it I found the puzzle in a School Mathematics Department on their Open Day so it also fits under Mathematics.

BTW the print photographed is