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?