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A cube that measures 3 cm on each side would consist of 27 cubic centimeters of ice.
If you were to picture the ice cube as a grid, you have the length and width of 3, so a single section is 9, since the depth is also 3, you triple the sections to result in 27.
Since you are dealing with cubic dimensions you would refer to the units as 27cm^3
(If you were simply dealing with 2 dimensions, such as 3x3, it would be 9cm^2)