Henry Ernest Dudeney/Modern Puzzles/145 - A Cube Paradox

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Modern Puzzles by Henry Ernest Dudeney: $145$

A Cube Paradox
I had two solid cubes of lead, one very slightly larger than the other.
Through one of them I cut a hole (without destroying the continuity of the four sides)
so that the other cube could be passed right through it.
On weighing them afterwards it was found that the larger cube was still the heavier of the two.
How was this possible?

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