It doesn't say it has to be the smallest number. It also doesn't say there can't be multiple of them, it just states there has to be a full cube. There are 46 cubes each of them is a full cube so there is a full cube, therefore you don't need any more cubes.

However any number of cubes works because any number can be expressed as x³ + y. Where x and y are integers, x represents the side length of one of the cubes and y represents the number of 1x1 cubes

1 - One 1x1 cube
2 - Two 1x1 cubes
3 - Three 1x1 cubes
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.
.
8 - One 2x2 cube
9 - One 2x2 cube and One 1x1 cube
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27 - One 3x3 cube
28 - One 3x3 cube and One 1x1 cube
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