NUMBER JIG

What is the lowest number that can be expressed as the sum of two different cubes in two different ways, known as the Hardy-Ramanujan number? Fit these numbers into the grid. One number doesn’t fit. This is the prize answer.

3 digits 107 170 265 346 530 735 762

785 900 955

4 digits 1511 1687 1729 2351 2451 3690 5013 5675 5874 6340 7861

5 digits 12342 17245 22527 29655 36728 43117 65611 65985 71957 75962 77180 85208

6 digits 450265

537375 574430 665989 721495 756311 797903

7 digits 3699972 3817565 7675754

8 digits 24958118