  We prove the exponential estimate
  \begin{equation*}
  P \{ s < \tau < \infty \} \leq C e^{-q s}, \quad s \geq 0, \end{equation*}
where $C, q >0$ are constants and $ \tau $ is the extinction time of the
supercritical branching random walk (BRW) on a cube. We cover both the
discrete-space and continuous-space BRWs.
