A solid cube is cut into 8 identical cubes. What is the percentage increase in the total surface area? 

100%

If side of larger cube = 2x

then to cut 8 identical cubes, side of smaller cube = x

Total surface area = 6 (side)²

Now,

            Large   :    One Small Cube

Side :      2       :         1

T.S.A:     6(2)²  :      6(1)²

                4      :       1

            Large   :    8 Small Cubes

T.S.A. :     4       :   (1 × 8) 

                4      :       8

                1      :       2

Total surface area increase by  = 2 - 1 = 1

Increase percentage = \(\frac{1}{1}\) × 100 = 100%