Can I use #6 wire to feed a sub panel off main
You can feed as many 100A subpanels as you want with #6 wire, as long as the wire is supplied from 60A breakers.   Breakers protect wires.  You need a 60A breaker to protect #6 wire.  (or #4 Al). 

In fact you can use any size of subpanel whose amp rating is >= the breaker that is feeding it.  Upsizing the panel is a very good idea  if it means getting more spaces.  Always get so many spaces that you never need twins/double-stuff breakers -- you can never have enough spaces!  42 spaces is not too many! 

The required size for subpanel feeder is exactly the same as the required size for branch circuits, and comes out of NEC table 310.15(b)(16), formerly 310.16.  Do not use the service drop/lateral table, those are outside and can't burn your house down obviously. 

You need 4-wire cable to feed a subpanel.  It is both illegal and unsafe to supply hot-hot-neutral (ungrounded) to a subpanel.  However, 3-wire cable can be used to a subpanel that is 240V-only and supports no 120V or 120/240V loads whatsoever -- for example water heater, A/C unit or any of those 8' baseboard heaters.  If you are stuck with useless 3-wire cable, sell it on Craigslist and let someone else use it. 

If you have individual wires (THHN) also keep in mind your neutral must be natively white and your ground must be green or bare.   Different deal for wire #4 or larger, as it can be "re-defined" using black, red, white or green tape.  

If you want to buy the correct wire for serving the panel from a 100A breaker, buy #3 Cu or preferably #1 Al.