492 Cubed is Sum of 3 Positive Cubes in 13 Ways/Historical Note

Historical Note on 492 Cubed is Sum of 3 Positive Cubes in 13 Ways
The question was asked in of January $1957$ for a (positive) integer less than $1000$ whose cube could be expressed as the sum of $3$ cubes in $5$ distinct ways.

A solution submitted by returned some $47$ such integers which have between $5$ and $9$ such expressions, but surprisingly $492$ was not among them.

$870$ had most such representations, that is, $9$.

Subsequent investigation unearthed several more.

By the time reported in his  of $1966$, there were $2$ integers each with $10$ such representations (that is, $492$ and $870$), and one had $11$ (that is, $792$).

The representations for $492$ and $792$ were found by, while the representations for $870$ were, as for the $1957$ investigation, attributed to.

A more recent investigation, using a computer program designed to test exhaustively all integers less than $1000$ has revealed that each of $492$, $792$ and $870$ has exactly $13$ such representations.