$\operatorname{Var}\hat\beta=\sigma^2/\sum(X_i-\bar X)^2$, not $\sigma^2/\sum X_i^2$

For a simple linear regression $Y_i=\alpha+\beta X_i+\varepsilon_i$, $\varepsilon_i\sim$ iid $(0,\sigma^2)$, with least squares fit $\hat Y_i=\hat\alpha+\hat\beta X_i$ and residuals $e_i=Y_i-\hat Y_i$, which statement is not true?