$\begin{array}{l}\text { 6. } 65^{1000}-8^{2001} — 0 \text { (fill in “>” “<” or } \\ \text { “ ”). }\end{array}$
6. >.

Notice,
$$
\begin{array}{l}
65^{1000}-8^{2001}=65^{1000}-8 \times 64^{1000}, \\
\left(\frac{65}{64}\right)^{1000}>1+\frac{1000}{64}>8 . \\
\text { Therefore } 65^{1000}>8 \times 64^{1000} \Rightarrow 65^{1000}-8^{2001}>0 .
\end{array}
$$