GAUSS7 2019 Problem 25

An 8 \times 8 \times n rectangular prism is made up from 1 \times 1 \times 1 cubes. Suppose that A is the surface area of the prism and B is the combined surface area of the 1 \times 1 \times 1 cubes that make up the prism. What is the sum of the values of n for which \frac{B}{A} is an integer?

Answer Choices
A. 86
B. 90
C. 70
D. 78
E. 96