Can I use a 7 speed shifter on an 8 speed cassette
The 7 and 8 speed cassettes have slightly different spacing (see http://sheldonbrown.com/cribsheet-spacing.html), so the derailleur will be slightly, almost unnoticeably, out of adjustment at largest and smallest cogs. And of course you won't be able to shift to one of the cogs.

If you can't change the shifter to 8-speed, you can install a 7-speed cassette on 8-speed hub with a spacer. 

The 8-speed hub is wider than 7-speed, so you will also need to bend the rear fork slightly to install the wheel.