It is really quite simple
Ohm's Law says that in any resistive circuit the Current in Amps (I) is directly proportional to the voltage (V) applied. The value of the resistance is the ratio of Voltage to Current
V/I = R or V=IxR
In other words in any one resistive circuit doubling voltage doubles the current.
Power is defined in Watts (W) and W = V x I so doubling the voltage from V to 2V results in Current equal to 2I thus power is 2V x 2I =4VI ie doubling the voltage results in 4 times the power.4 times the original power