The problem is not to enumerate or find the set of numbers that are sums of cubes. The conjecture is: every integer that is not of the form 9k+4 or 9k+5 can be

The problem is not to enumerate or find the set of numbers that are sums of cubes. The conjecture is: every integer that is not of the form 9k+4 or 9k+5 can be expressed as the sum of 3 cubes (and, in infinitely many ways).