If each edge of a cube is doubled, then the percentage increase in its total surface area is

1. Let the original edge length of the cube be $a$. The original total surface area ($A_1$) is:
$$A_1=6a^2$$
If each edge is doubled, the new edge length becomes $2a$. The new total surface area ($A_2$) is:
$$A_2=6(2a{)}^2=6(4a^2)=24a^2$$
The increase in surface area is:
$$\Delta A=A_2-A_1=24a^2-6a^2=18a^2$$
The percentage increase is calculated as:
$$\text{Percentage Increase}=\left(\frac{\Delta A}{A_1}\right)\times 100=\left(\frac{18a^2}{6a^2}\right)\times 100=3\times 100=300\%$$