It means the volume equivalent to a cube with a side length of one centimeter.
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One exactly
1cubic meter =1 000 000cubic centimeter
One cubed decimeter equals one liter. One cubed centimeter equals 1/1000 liter or one Milliliter (mL).
It isn't clear what "units" you are talking about.
1 cubed centimeter is equal to 1 mililiter. The only difference is that milliliters are typically used for liquids and cubed centimeters are more often used for solids.