Three-digit powers of $2$ and $5$ are used in this "cross-number" puzzle. What is the only possible digit for the outlined square?
\[\begin{array}{lcl} \textbf{ACROSS} & & \textbf{DOWN} \\ \textbf{2}.~ 2^m & & \textbf{1}.~ 5^n \end{array}\]

$\text{(A)}\ 0 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8$
The $3$-digit powers of $5$ are $125$ and $625$, so space $2$ is filled with a $2$.
The only $3$-digit power of $2$ beginning with $2$ is $256$, so the outlined block is filled with
a $\boxed{\text{(D) 6}}$.