Square of Hypotenuse of Pythagorean Triangle is Difference of two Cubes/Mistake

Source Work

 * The Dictionary
 * $13$
 * $13$

This statement does not appear in the first edition of of $1986$.

Mistake

 * The square of the hypotenuse of a right-angled triangle is also the difference of $2$ cubes; thus, $13^2 = 8^3 - 7^3$.

Correction
This is not true for all right-angled triangles.

The most immediate counterexample is the $3-4-5$ triangle, whose hypotenuse is $5$.

The sequence of positive integers whose squares are the difference between $2$ cubes begins:
 * $13, 28, 49, 104, 147, 181, 189, 224, 351, 361, \dotsc$