In the SI system, you'll find . . .
liter
cubic meter
milliliter
cubic centimeter.
But the 'customary' system is where you'll find
cubic inch
cubic foot
cubic yard
fluid ounce
cup
pint
quart
gallon
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By definition, a unit cube has a volume of 1. "Unit" means 1 so if the volume was not 1 it would not be called a unit cube!
The primary unit of metric volume is the liter (L).
Volume is measured in decibals.
Cubic inches or cubic meters. Take any unit of length and cube it and that is a unit for volume
The "cubic centimeter" is a unit of volume.