Double Cube Roots

Algebra Level 2

640003+64000+3(1640)+13\sqrt{\sqrt{\sqrt[3]{\color{#3D99F6}{64000}} + {\sqrt[3]{\color{#3D99F6}{64000} + \color{teal}{3(1640) + 1}}}}}

With the assistance of the algebraic identity (a+b)3=a3+b3+3ab(a+b) (a+b)^3 = a^3 + b^3 + 3ab(a+b) , evaluate the above expression.

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