If you run the contour walker for N=2, you will get a lot of hits for a sum of 2, for instance:

- 49^3-47^3-24^3
- 163^3-161^3-54^3
- 385^3-383^3-96^3
- 751^3-749^3-150^3
- 1297^3-1295^3-216^3
- 2059^3-2057^3-294^3
- ...
- 10841593393^3-10841593391^3-8901144^3
- ...

10,841,593,393 was the largest value found when I stopped the search.

Inspection reveals that these are all of the form (6n^3+1)^3-(6n^3-1)^3-(6n^2)^3. The above list starts with n = 2.

Clearly, it you take all the terms of a sum from the previous section (that yields 2) and multiply them by 'm', the sum will be 2m^3, so there is a simple series that can generate an infinite number of examples of any sum of this form.

(c) John Whitehouse 2021