Find all integers $a,b,c$ such that $0 \le a,b,c \le 1000$ and $1001|a^3+b^3+c^3-3abc-1$

Question

Find all integers $a,b,c$ such that $0 \le a,b,c \le 1000$ and $1001|a^3+b^3+c^3-3abc-1$ We have to check divisibility of $7,11,13$ and we may use the identity $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ But I can't approach further. Help!