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Side = 3 units, volume = 27 cu units, side = 6 units, volume = 216 cu units.

The side is increased by a factor of 2 and the volume is increased by a factor of 8, ie 23

If the side were increased by a factor of 3, we would thus expect the volume to increase by a factor of 33 ie 27, so: side 9 units, volume 729 cu units which is indeed 27 x 27.

To summarise: the volume increases by the cube of the factor by which the side increases.

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