8. For a real number $x$, $[x]$ denotes the greatest integer not exceeding $x$. For some integer $k$, there are exactly 2008 positive integers $n_{1}, n_{2}, \cdots, n_{2008}$, such that $k=\left[\sqrt[3]{n_{1}}\right]=\left[\sqrt[3]{n_{2}}\right]=\cdots=\left[\sqrt[3]{n_{2008}}\right]$, and $k$ divides $n_{i}(i=$ $1,2, \cdots, 2008)$, then $k=$ $\qquad$
8. 668 Detailed Explanation: If $\sqrt[3]{n}-1n$, satisfies $k$ divides $n$, then $n$ can take $k^{3}, k^{3}+k, \cdots, k^{3}+3 k^{2}+3 k$, a total of $3 k+4$ values, so $3 k+4=2008, k=668$.