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Cubed is the third dimension because it is a cube. A cube has three dimensions of equal amount. A cube of three-inch sides, to get its volume you'd multiply three times three times three, which is three cubed.
3x3x3 = 27
27
9 cubed is equal to 729.
15 cubed means 15 times itself three times (15x15x15). 15 cubed is equal to 3,375.