UMVUE of the Poisson mass at zero times cube

Let $X_{1},X_{2},…,X_{n}$ $(n\ge 3)$ be a random sample from $\mathrm{Poisson}(\theta)$, where $\theta\in(0,\infty)$ is unknown and let $$T=\sum_{i=1}^{n}X_{i}.$$ Then, the uniformly minimum variance unbiased estimator of $e^{-2\theta}\theta^{3}$