Digit Cubes

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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