Why is a cube root called a cube root?

Because it was discovered by Jaques Cube when he was using his calculator while walking and he tripped over a root and accidentally hit the square root key, then a number, then ^ carrot key, then hit 1 divided by 3 then enter while he was falling

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The non-idiotic answer is that the volume of a cube is a side times a side times a side (a side cubed). Calculating the cube root is the inverse function of cubing, the root being the basic part you started with, a side.