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A cubic centimeter is a measure of volume. 1 cubic centimeter is often referred to as a cc, or cm^3. 1 cc is also (usually) equal to 1 milliliter (ml) of water.
You can't compare one with the other. A cubic centimeter is a unit of volume, a centimeter is a unit of length. When you thus have different kinds of incompatible units, you can't add them, subtract them, compare them, or convert one to the other.
There is no equivalence. A centimetre is a measure of length or distance in 1-dimensional space while a millilitre is a measure of volume in 3-dimensional space. The two measure different things and, according to basic principles of dimensional analysis, conversion from one to the other is not valid without some addition information.
1 mL = 1 millilitre (measure of volume) 1 cm = 1 centimetre (measure of length) 1 cm^3 = 1 cubic centimeter (measure of volume) 1 ml = 1 cm^3
L is a measure of volume, while cm is a measure of distance. A cubic centimeter, written both as cc and cm^3, is a measure of volume, and 1 cc = 1 mL = 0.001 L