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

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I was told this was impossible to solve, but I'm not one to shy away from a challenge. A bit tricky, perhaps, but that's what makes it so intriguing. We all know Pythagoras' famous theorem found its roots in 3x3 + 4x4 = 5x5 (the classic right-angled triangle formula), but did you know that 3x3x3 + 4x4x4 + 5x5x5 = 6x6x6? This puzzle is a game-changer - it shows you can either create all three 3x3x3, 4x4x4 and 5x5x5 cubes or use every piece to make a single 6x6x6 cube. I categorized this under Toys/Puzzles, but after stumbling upon it in a School Mathematics Department on their Open Day, I realized it also falls under the umbrella of Mathematics. By the way, the print you see here is one of my early attempts, and as you can tell, it's a bit on the small side. A more recent print, done with better equipment, turned out even better.