MATHEMATICS : A FUNNY FACT

India's Ramanujan was a genius personality in mathematics though he did not get proper education in an organised manner. He had discovered a surprising and funny fact about 'cubes of numbers'.

There is only one possible case
in which one can equate the sum of cubes
of two different positive integers
with the sum of cubes of two
altogether different positive integers.
There is no other such case known till now.

The sum of cube of 1 and cube of 12
is equal to the sum of cube of 9 and cube of 10.
The sum is 1729 for both.
Try to find out if there be any
possibility by which you can relate
four different positive integers
in the similar fashion.