  In Ramanujan's Lost Notebook there is an amazing identity that furnishes
infinitely many "almost counterexamples" to the cubic Fermat's Last Theorem,
with no indication whatsoever how he discovered it. In 1995, Michael Hirschhorn
explained, in a brilliant way, how Ramanujan may have done it, based on a
certain polynomial identity for a sum of four cubes. Much earlier, Eri
Jabotinsky, in an article published in 1946 (in a mathematics journal for
teenagers) explained how Ramanujan may have discovered these polynomial
identities needed for Hirschhorn's approach. Here we combine these two
brilliant ideas (that may or may not have been how Ramanujan did it), automate
it, and generalize, by developing an algorithm to solve a large class of cubic
diophantine equations. Our interest in this problem was rekindled after reading
Amy Alznauer's (b. Andrews) delightful children book "The Boy Who Dreamed of
Infinity" (Candlewick Press), 2020, where Ramanujan's identity appears in one
of the illustrations.
