Millimeters are a measure of length, while cubic centimeters are a measure of volume. Because of this, the two scales are not strictly analogous and cannot be exchanged without conversion of two-dimensional length to a three-dimensional volume. Both units are metric, however, and so further conversion is unnecessary.
A cubic millimeter is one-tenth of a cubic centimeter. Assuming a volume of 10 mm^3, therefore, allows a conversion to 1 cc. For any conversion of this type, it is always essential that both units express the same concept. Volume can only be converted to volume, area to area and length to length.