Do I report the taxes that Airbnb pays to local and state government on my behalf?

[Carl]

It depends. Are the taxed paid "on your behalf" included in the 1099-MISC you receive from AirB&B in the total amount they pay to you?

If yes, then you can claim those taxes.

If no, then you can not claim them, as they are not included in the income reported as being paid to you by AirB&B.