To change volume to cm^3 permanently in your sheet you additionally would have to go again to Tools/Worksheet options/Unit system then to "Derived Units", chose "Volume" and click remove.
But you don't have to change the unitsystem if you just want single results to be displayed using non-SI units.
If you click in the result of a calculation like ni(300K)=..., you see a small black square placeholder after the unit. Just type in the unit you want to see there - in your case 1/cm^3 - and press enter.