Depends what size the cup is :/
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1 gallon = 16 cups 1 cup =0.23 gallon
Millimeters (mm) measure distance, while cups measure volume. The two are not compatible.
128 floz/gallon 8 floz/cup 128*2/8=128/4=32 cups
You would use millimeters for the measure of the capacity of a paper cup.
If you mean a cup as in "a cup of flour or sugar" you cannot convert cups to millimeters as a cup is a measure of volume were as a millimeter is a measurement of length. It cannot be converted.