If the edge of a cube is increased by $25\%$, then the percentage increase in its surface area is:

The surface area of a cube is given by $A=6a^2$, where $a$ is the length of an edge. Since $6$ is a constant, the surface area depends on the square of the edge ($a^2$).
We can use the successive percentage formula for $a\times a$:

$$\text{Percentage Increase}=x+y+\frac{xy}{100}$$

Here, $x=25$ and $y=25$:

$$\text{Percentage Increase}=25+25+\frac{25\times 25}{100}=50+\frac{625}{100}=50+6.25=56.25\%$$