A solid cube is made of white plastic and has dimensions n\times n\times n, where n is a positive integer larger than 1. The six faces of the cube are completely covered with gold paint. This cube is then cut into n^3 cubes, each of which has dimensions 1\times1\times1. Each of these 1\times1\times1 cubes has 0,1,2, or 3 gold faces. The number of 1\times1\times1 cubes with 0 gold faces is strictly greater than the number of 1\times1\times1 cubes with exactly 1 gold face. What is the smallest possible value of n?
Answer Choices
A. 7
B. 8
C. 9
D. 10
E. 4