Sorry, but your understanding of physics is a little lacking.
The power requirements have nothing to do with gearing, but wind and rolling resistance only.
With larger tyres giving higher gearing, there is no more power required. It makes the engine run at a lower speed. Whether or not that affect mileage deends on the engine. Engines have an efficiency curve and provide maximum efficiency at certain speeds. For most diesels, higher gearing on the motorway reduces fuel consumption as the higher gearing put the engine closer to its maximum efficiency point. This is why people fitting overdrives find a reduction in fuel consumption. For most engine, maximum efficiency is found near the peak torque point.
The problem with the OP's question is complicated. The gearing increases (which is good), but the wind resistance increases at the same time. In addition, the power required to accelerate the tires increases (slightly).
Where most people get confused is that they use the odometer to check mileage. If you change tyres, the odometer reads incorrectly and it appears that mileage changed quite a bit. Larger tyres make the odometer slow down, so it seems that the fuel consumption increased. If you adjust the mileage figures for the odometer error, you'll fnd little difference.