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Find the greatest 3-digt number (the first is not 0) where $\overline { abc }$ is the number and:

${ a }^{ 3 }{ +b }^{ 3 }{ +c }^{ 3 }=100a+10b+c$

For example, $153$ satisfies the conditions since ${ 1 }^{ 3 }{ +5 }^{ 3 }{ +3 }^{ 3 }=153$.

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