Let $X\_1,..,X\_n$ be independent and $Bin(1,\theta)$ distributed. I would like to find the UMVUE for $\phi(\theta)=\theta^3$. I have a complete and sufficient statistic in $T=\sum\_iX\_i$, and a unbiased estimator in $S=X\_1X\_2X\_3$. I've tried to apply Rao–Blackwell:

$$\mathbb{E\_{\theta}}(X\_1X\_2X\_3\mid T)$$

I'm not sure how to proceed as the individual terms are not indenpendent with T.