No, there is no type of deduction for back taxes paid on your federal return. If you file a state tax return, there "may" be some benefit for federal taxes paid. You'd need to check your state tax return instructions to find out for sure.
*** I am NOT a tax expert. I am a seasoned TurboTax user, and volunteer to provide assistance to TT users. Nothing I post is to be considered TAX ADVICE; I bear no legal liability for responses.***