A cubic unit is essentially a three-dimensional unit used to describe volume, just like a square unit is a two-dimensional unit that describes area.
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I assume that with "capacity" you mean the measurement that is officially known as "volume". The standard unit of volume is the cubic meter. The liter (1/1000 of a cubic meter) and the milliliter = cubic centimeter (1/1000 of a liter) are also often used.
The cubic space inside a shape
If you mean capacity in the sense of volume, the main unit would of course be the cubic meter; other units used include cubic decimeters (equal to liters), cubic centimeters, cubic millimeters.
a liter means a unit of volume
a unit of linear measure