There is no six-core spec model Mid-2010, but there is one for Mid-2012.
The Mid-2010 has different processor configurations, neither of them six.
(Either four-core or eight, is what shipped in the Mid-2010 sales model)
If your computer shipped with Lion 10.7, it would be one of these versions,
and that is only if your Mac Pro is the Mid 2010. (not six core)
Original OS Mac OS X 10.6.4 (10F2521, 10F2554)
Later OS Mac OS X 10.7 (11A511a), 10.7.2 (11C74), 10.7.3 (11D2001)
Double check the model build series sales information & identify this correctly.
This would be Mac Pro (Mid-2012) with either Four, Six or Twelve core processor:
Original OS Mac OS X 10.7.3 (11D2001)
Later OS OS X 10.8 (12A269), 10.8.3 (12D78)
as noted from http://mactracker.ca specs and http://everymac.com online info
You should be able to match the serial number with the model sales spec to see
what was shipped with the computer. I've asked the host to move your Mac Pro
post to there, since it is not a PowerMac G5 architecture; yours runs Intel cores.
Good luck & happy computing! 🙂