Cubic centimeters measure volume. Centimeters measure length. Think in terms of the difference in measuring how much milk you want to buy compared to how tall you are.
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Square centimeters is a measure of surface area. Cubic centimeters are a measure of volume. A cube that's 20 cm on an edge would have 6 surfaces, each 400 square cm in size, giving a total surface of 2400 square centimeters - slightly less than 1/4 of a square meter. That same cube would have a volume of 8,000 cubic centimeters (which would be 8 liters.)
Since there are 1,000 cubic centimeters to one liter, 66.3 liters = 66,300 cubic centimeters.
17.82 meters or 1782 centimeters.
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The side length of this cube is 3 centimeters. The volume is 3 centimeters times 3 centimeters times 3 centimeters = 27 cubic centimeters.