I am prescribed 20mg oxcycontin 3 a day it only last about 5hrs. Should I increase the mg dose or take another 20mg ever 6 hrs instead of every 8 hrs?

Neither. It depends on the reason your doctor prescribed the medication. If you are having breakthrough pain your condition may warrant further investigation. In any event you should not take more than what was prescribed.
Dont change on own. You should never change your pain medicine on your own. When patients do that in most practices it is grounds for dismissal. Check with your doctor before making any changes and make sure that the doctor agrees.