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Cubing Near a Base (Yavadunam)

Cube numbers like 102 or 997 without long multiplication

The Rule

  1. 1Find d = number − base (base 100 or 1000; d is negative below the base).
  2. 2The cube is written in three parts: (n + 2d) | 3d² | d³.
  3. 3The middle and right parts each take as many digits as the base has zeros.
  4. 4Carry any extra digits to the left; a negative right part borrows from the left.