You asked:

Is a cubic centimeter the same as a liter?

No

A cubic centimetre or cubic centimeter, the commonly used unit of volume extending the derived SI-unit cubic metre and corresponds to the volume of a cube measuring 1×1×1 cm. One cubic centimetre corresponds to a volume of of a cubic metre

The litre (or liter see spelling differences), the unit of volume equal to 1/1,000 cubic metre or 1 cubic decimetre (dm)

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