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Examine if 130 is a perfect cube .If not...

Examine if 130 is a perfect cube .If not then find the smallest number that must be substracted form 130 to obtain a perfect cube

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130-1=129,129-7=122-19=103,103-37=66,66-61=5
The next number to be subtracted is 91 which is greater than 5. Therefore the process of successive substraction does not give zero Hence 130 is not a perfect cube. If we subtract 5 from 130 the above process will give zero after 5 successive subtraction
Therefore 130-5=125=`5^(3)`
Thus 5 is the required number
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