ON FOUR TUPLE OF DISTINCT INTEGERS SUCH THAT THE SUM OF ANY TWO OF THEM IS CUBE OF A POSITIVE INTEGER

In this article we have discussed determination of distinct positive integers $a,b,c,d$ such that $a+b, a+c, b+c, a+d, b+d, c+d$ are cubes of positive integers with \\

(i) at least three numbers, say $a,b,c$ are positive.\\

(ii) all four numbers $a,b,c,d$ are positive.\\

We can obtain infinitely many four tuples from a single four-tuple.