I do not claim credit for this puzzle; I saw it online years ago and realised it hadn't been asked here yet (as far as I could tell), so I thought I'd share it with the community here. I cannot recall the text verbatim, so I sincerely hope that I do not end up being misleading. Here goes:
You start with small and equal cubes, 27 of which are put together to form a large cube. How does one then remove 1 from the middle of the large cube to leave only 26, while not touching any of the sides of the large cube?
Maybe this is a large cube and if you take away the middle one you get 26.
The $216$ is $6$ cubed ($6^3$) made of $27$ small cubes.
Taking away the middle '1' leaves "2 6".
Edited by asker:
Cubes in the puzzle are used in a figurative sense. Start with 27 small cubes: 2^3 = 8. Put them together to form a large cube: 8*27 = 216 = 6^3. You are now free to remove 1 from the middle and leave 26 behind, all without touching any of the sides!
The cube is formed floating in a vacuum with only the corners of one of the smaller cubes ever touching any other of the smaller cubes. The cube itself is half cube matter, and intermittently half cuboid empty space. A small cube in the middle of this scenario can come out of the center of the larger cube.
Edit: Using pincer utensils to go through the 'gaps' of the cube you can avoid touching the sides. Then manipulating the cube carefully or shaking it will remove the middle cube if it is not connected at its corners, cut it out if it is.
As it's stated you can build a larger cube from there so in principle they are not built up in the larger one. Just remove 1 of those magnetic cubes from the group (implying you won't use it) and just build up your larger cube with the 26 small cubes, leaving a vacant in the middle of the structure.
the literal product
1 X 1 X 1 ........X 1 such that there are 27 1's multiplied together. This would result in a cube(1). You could remove one the central 1 leaving 26 cubes (1)
without touching the sides?