Easy does it! The Smart Scholar Method

Take the series of perfect cubes 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.

Look at the digit-roots (successive sum of the digits till reduced to a single digit) of this series.

They are 1, 8, 9, 1, 8, 9, …The digit-root has to be one among 1, 8 and 9.

The digit-root of 989683052 is 9 + 8 + 9 + 6 + 8 + 3 + 0 + 5 + 2 = 50 > 5 + 0 = 5.

The digit sum when 9, 8, 1, 3 and 6 are suffixed would be 5, 4, 6, 8 and 2 respectively.

Of these, the only possibility is 3 (which gives the digit-root 8).

Caution! The converse is not true. In other words, just because the digit-root is 1 or 8 or 9, it does not follow that the number is a perfect cube. Take 19 or 107 or 108 for example.

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