Is one cubic centimeter the same as one milliliter?

They are equal volumes.

1 cubic meter = (100 cm)3 = 1,000,000 cubic centimeters

1 cubic meter = 1,000 liters

1,000,000 cubic centimeters = 1,000 liters

1,000 cubic centimeters = 1 liter

1 cubic centimeter = 1 thousandth of a liter = 1 'milli'liter