Find the sum of all ordered pairs of positive integers such that both and are perfect cubes.
If none such pair exists then enter 0.
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Assume the contrary.Let, 3 m + n = a 3 and 3 m 2 + n 2 = b 3 . Multiplying them and some algebra gives, ( 2 m ) 3 + ( m + n ) 3 = ( a b ) 3 which contradicts the fermat's last theorem. Hence,no such pair exist and the answer is 0.