Dissecting a Cube: Upper Secondary Mathematics Competition Question

This week we have been looking at the sums of squares; here is a problem regarding the sums of cubes.

You have a cube with sides of length 5 units. You need to dissect it into smaller cubes, all with integer sides, in such a way that you can reconstruct the original cube. What is the minimum possible number of smaller cubes? List how many cubes of each size there are.

Remember that it is not enough for the sums of cubes to be arithmetically correct, the cubes need to all fit together to make the original cube with sides of length 5 units.





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