cubical relations

One cube is equal to sum of three cubes

According to Fermat, a³  +  b³  =  c³   is not possible with a,b,c are all positive integers. However, one cube can be expressed as a sum of three cubes.

6³  = 5³  + 4³  + 3³

9³   = 8³  + 6³  +  1³

20³  = 17³  + 14³ + 7³

25³  =  22³ +  17³  + 4³

28³  = 21³  + 19³  + 18³

58³  = 49³  + 42³ + 15³

70³ = 57³  + 54³ + 7³

210³  = 171³  + 162³  + 21³

214³  =  213³ + 51³  + 16³

256³  = 255³  + 57³  + 22³

256³  = 255³  + 27³  + 22³

298³  = 297³ + 64³  + 15³

682³  = 675³  + 213³  + 16³

1062³  = 1059³  + 213³  + 108³

1408³  = 741³  + 675³  + 346³

2176³ = 2169³  + 447³  + 214³