Milliliters and cubic centimeters mean a volume and gram means a weight.
Only for pure water we can say:
1 milliliter or 1 cubic centimeter of water weighs 1 gram.
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A gram is a measure of mass, not weight.
But leaving that aside, the parity for pure water is only approximately true. Until 1964 a litre was defined as the volume of one kilogram of pure water at 4 degrees Celsius and at a pressure of 760 millilitres of Mercury. With that definition a conversion would have been valid - but only under those conditions. In any case that definition of a litre was abandoned in favour of 1 litre =1000 cubic centimetres and with that definition 1 ml of pure water has a mass of 0.9999720 grams. Not quite 1 gram!
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