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1 cm3 / cc = 0.0042 cup
1 cup = 236.59 cm3 / cc
Definition of cubic centimeters of water provided by WikiPedia
One cubic centimetre corresponds to a volume of 1 / 1,000,000 of a cubic metre, or 1 / 1,000 of a litre, or one millilitre (1 cm3 ≡ 1 ml). The mass of one cubic centimetre of water at 3.98 °C (the temperature at which it attains its maximum density) is closely equal to one gram.
Definition of US cup of water provided by WikiPedia
Pne U.S. cup of water weighs approximately 81⁄3 avoirdupois ounces. Since an imperial cup of water weighs approximately 10 avoirdupois ounces and five imperial cups are approximately equal to six U.S. cups