Variance of the exponential of a gamma

Let $X \sim \text{Gamma}(\text{shape } 8,\ \text{scale } \tfrac13)$. Compute $\operatorname{Var}(e^{X})$. The answer has the form $a^{b} - \left(\tfrac{a}{2}\right)^{c}$ for integers $a, b, c$; find $a\cdot b\cdot c$.