In this article we further develop methods for representing integers as a sum
of three cubes. In particular, a barrier to solving the case k=3, which was
outlined in a previous paper of the second author, is overcome. A very recent
computation indicates that the method is quite favourable to other methods in
terms of time estimates. A hybrid of the method presented here and those in a
previous paper is currently underway for unsolved cases.Comment: 4 page