The percentage increase in the surface area of a cube when each side doubled is

Let the initial edge length of the cube be $x$.
The initial surface area is given by:

$$A_1=6x^2$$

When each side is doubled, the new edge length becomes $2x$.
The new surface area is given by:

$$A_2=6(2x{)}^2=6(4x^2)=24x^2$$

The increase in surface area is:

$$\Delta A=A_2-A_1=24x^2-6x^2=18x^2$$

The percentage increase is calculated as:

$$\text{Percentage Increase}=\left(\frac{\Delta A}{A_1}\right)\times 100\%=\left(\frac{18x^2}{6x^2}\right)\times 100\%=3\times 100\%=300\%$$