Question concerning Battery voltage and capacity

Lets say we have two batteries, one that is 4.2V with a capacity of 500mAh and another 8.2V battery with the same capacity. What i cant get through my head is when i want to charge both batteries at lets say 500mA, woudnt the 8.2V require twice as much power because the voltage input will be bigger(twice as much) and P=VI. I know that it wouldnt, but could someone explain to me why that is?

thanks

Sure, the battery with the higher voltage will need more power to charge it. It will also give more power when it discharges but its capacity is the same as the lower voltage battery.
The battery with the higher voltage (and higher power) will also be bigger.