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There are videos on YouTube (Mathologer or Numberphile come to mind) but, the trick is to look at the area -- notice that the pieces are not fully contained the first two times, only at the end it seems a tight fit.
See it as the tinfoil wrapper around your chocolat bar. It takes almost no space and the bar plus wrapper fit nicely in the outer paper wrapper.
Now take that tinfoil and crunch it into a cube. Same volume but now it wouldn't fit.
If it's so easy, can you make me one?
Okay!!!
You still have the sound turned on? I turned it off months ago.