492 is Sum of 3 Cubes in 3 Ways/Mistake

Source Work

 * The Dictionary
 * $492$
 * $492$

Mistake

 * $492$ is the sum of $3$ cubes, one or two of which may be negative, in no fewer than $10$ different ways. [Madachy]

Correction
appears to have conflated $2$ separate results.

The number of known ways $492$ can be expressed as the sum of $3$ cubes, either positive or negative, is $3$:

The result given in 's $1966$ work is that it is possible to express $492^3$ in no fewer than $10$ different ways:

(except that the $5$th expression is incorrect: $144$ should read $114$).

Three further such expressions for $492^3$ have since been found:

$492$ is not the only integer whose cube can be expressed as the sum of $3$ positive cubes in $13$ ways, but it is the smallest.

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