8. For integer $n \geqslant 3$, let $n!=\prod_{i=1}^{k} p_{i}^{\alpha_{i}}$, where $p_{1}, p_{2}, \cdots, p_{k}$ are all prime numbers, and $p_{1}<p_{2}<\cdots<p_{k}$, $\alpha_{1}, \alpha_{2}, \cdots, \alpha_{k}$ are all positive integers. Find all $n(n \geqslant$ $3)$ such that $\alpha_{1}, \alpha_{2}, \cdots, \alpha_{k}$ form a geometric sequence.