AMC 8 2014 Problem 19

A cube with $3$-inch edges is to be constructed from $27$ smaller cubes with $1$-inch edges. Twenty-one of the cubes are colored red and $6$ are colored white. If the $3$-inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white? $\textbf{(A) }\frac{5}{54} \textbf{(B) }\frac{1}{9} \textbf{(C) }\frac{5}{27} \textbf{(D) }\frac{2}{9} \textbf{(E) }\frac{1}{3}$