Correct Answer: 16 cm

Solution : Length of each side of the cube = 8 cm
Total surface area of the cube = 6a$^2$ = area of a square + 128 cm$^2$
Let's assume that the length of each side of the square is "x" cm.
Surface area of a cube = 6a$^2$
Area of a square = x$^2$
Total surface area of the cube = 6a$^2$ = 6(8$^2$) = 384 cm $^2$
Area of the square = x$^2$
According to the problem, 6a$^2$ = x$^2$ + 128
Substituting the value of 6a$^2$, we get:
384 = x$^2$ + 128
⇒ x = $\sqrt{(384 - 128)} = \sqrt{256}$ = 16 cm
Hence, the correct answer is 16 cm.