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.
Keywords and Phrases
Perfect squares, cubes, cubefree numbers, taxicab numbers, cubefree taxicab numbers, primes.
A.M.S. subject classiﬁcation