8. Given that $A B C D-A_{1} B_{1} C_{1} D_{1}$ is a unit cube, two ants, one black and one white, start from point $A$ and crawl along the edges. Each time they complete an edge, it is called “completing a segment”. The white ant’s crawling route is $A A_{1} \rightarrow A_{1} D_{1} \rightarrow \cdots$, and the black ant’s crawling route is $A B \rightarrow B B_{1} \rightarrow \cdots$. They both follow the rule that the $(n+2)$-th segment must be on a skew line with the $n$-th segment. Suppose both ants stop after completing 2008 segments at some vertex of the cube. At this point, the distance between the black and white ants is
8. $\sqrt{2}$.

It is easy to know that the routes taken by the two ants have a cycle of 6. After the black and white ants have completed 2008 segments, they stop at vertices $D_{1}$ and $C$ of the cube, respectively, with a distance of $D_{1} C=\sqrt{2}$.