Digit Cubes

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

a3+b3+c3=100a+10b+c{ a }^{ 3 }{ +b }^{ 3 }{ +c }^{ 3 }=100a+10b+c

For example, 153153 satisfies the conditions since 13+53+33=153{ 1 }^{ 3 }{ +5 }^{ 3 }{ +3 }^{ 3 }=153.

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