17. Let $[x]$ denote the greatest integer not exceeding $x$, for example $[3.15]=3,[3.7]=3,[3]=3$, then $[\sqrt[3]{1 \cdot 2 \cdot 3}]+[\sqrt[3]{2 \cdot 3 \cdot 4}]+[\sqrt[3]{3 \cdot 4 \cdot 5}]+\cdots+[\sqrt[3]{2000 \cdot 2001 \cdot 2002}]=$ $\qquad$
answer: 2001000