Cubes over the terminating denominators

Let $S$ be the set of positive integers $k$ for which $\tfrac1k$ has a terminating decimal expansion (e.g. $2 \in S$ since $\tfrac12 = 0.5$, but $7 \notin S$). Evaluate $\displaystyle\sum_{k \in S} \frac{1}{k^3}$.