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is it possible to construct a cube with 2000 interlocking cubes?
It depends. Do all the cubes need to be equally sized? A cube has 6 sides, or faces. 2,000 divided 6 is 333.3. So, yes, it could be possible if some of the cubes are divided into thirds. However, if all the interlocking cubes need to be equally sized, then no, it wouldn't be possible. It all just depends.
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