Let 'a' represent the length of the side, a>0.

Using the Pythagorean Theorem we can write:

(8 1/4)^2 = 2a^2

8 1/4 = (8*4 + 1)/4 = 33/4

2a^2 = (33/4)^2

a^2 = (1/2)(33/4)^2

a = 5.83 in

The total area of the cube is:

A = 6a^2

A = 6*(1/2)(33/4)^2

A = 204.109 in^2

The volume of the cube is:

V = a^3

V = 5.83^3

V = 198.16 in^3