List two non-si units for volume, and explain how they relate to the cubic centimeter.

The two non-SI units of volume are cubic feet (cu.ft) and gallon (gal). Cubic feet is mostly used while measuring gases and gallon is mainly used to measure liquids. These two non-SI units are definitely popular units of measurement.
The relation between cubic feet and cubic centimetre can be deduced by
1 foot = 2.54 cm X 12 inch/ft
         = 30.48 cm
So
1 cubic foot = 3 * (30.48 cm)
                   = 28317 cubic centimetre
The relation between gallon and cubic centemetre can be deduced by
1 gallon = 3.785 litres X 1000 cc/L
             = 3785 cubic centemetre.