A sugar cube manufacturer wants to sell 500 sugar cubes in a box also in the shape

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A sugar cube manufacturer wants to sell 500 sugar cubes in a box also in the shape of a cube.
a. Assuming there are no gaps in the box, explain why this will not be possible.
b. What is the closest number of cubes to 500 that he will be able to pack into a cube shaped box? Give a convincing reason for your answer.

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