Can we use \(a^3+b^3\) or \(a^3-b^3\) formula?

Algebra Level 4

\[\frac{(2^3-1)(3^3-1)(4^3-1)\cdots(1000^3-1)}{(2^3+1)(3^3+1)(4^3+1)\cdots(1000^3+1)}=\, ?\]

Submit your answer to three decimal places.

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