difference between neighbor cube and square

[ZAKIRS]

Dear all, 

as part of the d=m^p-n^q ("demping") problem, 

here is a list of possible d=m^3-n^2, d<1000,  m^3 is the smallest >n^2, 
that is d is the diffrence between a square and the next cube.
 
there are only 230 possible values of d <1000, 
but as usually for such  lists this one is also not full. 

i've checked it up to n=377725241, and  the largest n, 
involved in the list is n=223063247  being the smallest  n such that 
d=207 is a difference between n^2 and  the next cube.
Please note that 207 as the difference between  cube and square 
appears as early as 207=6^3-3^2,
but here cube and square are not neighbors.

Anybody can kindly add more terms, thanks, zak
 
{1, 2, 4, 7, 11, 13, 15, 18, 19, 20, 25, 26, 28, 35, 39, 40, 44, 45, 
  47, 48, 49, 53, 54, 55, 56, 60, 63, 67, 71, 72, 74, 76, 79, 81, 83, 
  87, 100, 104, 106, 107, 109, 112, 116, 118, 126, 127, 128, 135, 
  139, 143, 146, 147, 148, 150, 151, 152, 153, 155, 159, 170, 172, 
  174, 175, 180, 184, 186, 191, 193, 200, 207, 212, 215, 216, 233, 
  235, 236, 239, 242, 244, 249, 251, 252, 256, 261, 270, 277, 284, 
  286, 289, 292, 293, 298, 299, 301, 307, 308, 343, 348, 350, 355, 
  356, 359, 362, 364, 366, 368, 371, 375, 391, 405, 415, 424, 425, 
  431, 433, 439, 440, 447, 448, 455, 459, 464, 471, 476, 477, 495, 
  496, 499, 503, 506, 508, 511, 515, 516, 524, 535, 546, 550, 557, 
  566, 580, 583, 586, 587, 589, 593, 596, 599, 604, 612, 615, 618, 
  622, 631, 636, 639, 647, 648, 652, 663, 667, 673, 674, 676, 680, 
  683, 685, 688, 702, 703, 704, 718, 726, 727, 728, 732, 735, 741, 
  755, 756, 760, 764, 766, 767, 769, 775, 776, 782, 791, 797, 800, 
  802, 804, 828, 831, 832, 847, 850, 856, 859, 860, 866, 868, 875, 
  882, 888, 891, 892, 895, 900, 908, 914, 924, 927, 930, 931, 935, 
  944, 945, 954, 964, 968, 971, 973, 975, 980, 984, 991, 996, 999}

It seems that  a lot of values of d such that 3, 5, 8, 9, 12, 14, 
may appear for larger n, but who knows...