Magic Series for Cubes 
m3-approximation

Only magic square data were used to estimate the third members of the formulae.

Lower Orders: 9 correct digits (relative error < 3*10^-10)
Orders above 100: all 11 digits should be correct

N(040)= 7.2786050579*10^138 (exact: N(040)= 7.2786050559...*10^138 )
N(041)= 2.1732307797*10^143
N(042)= 6.8292984134*10^147
N(043)= 2.2558293460*10^152
N(044)= 7.8229479859*10^156
N(045)= 2.8449046432*10^161
N(046)= 1.0837278618*10^166
N(047)= 4.3198810891*10^170
N(048)= 1.8000572331*10^175
N(049)= 7.8333331924*10^179
N(050)= 3.5567481060*10^184
N(051)= 1.6835377734*10^189
N(052)= 8.3001979322*10^193
N(053)= 4.2588963507*10^198
N(054)= 2.2725304643*10^203
N(055)= 1.2600864608*10^208
N(056)= 7.2552968141*10^212
N(057)= 4.3348295454*10^217
N(058)= 2.6857130438*10^222
N(059)= 1.7243961302*10^227
N(060)= 1.1466562514*10^232
N(061)= 7.8919887696*10^236
N(062)= 5.6188025237*10^241
N(063)= 4.1358107666*10^246
N(064)= 3.1455790777*10^251
N(065)= 2.4707835213*10^256
N(066)= 2.0032781495*10^261
N(067)= 1.6757356799*10^266
N(068)= 1.4455040390*10^271
N(069)= 1.2852296861*10^276
N(070)= 1.1773184757*10^281
N(071)= 1.1106285044*10^286
N(072)= 1.0785013317*10^291
N(073)= 1.0776313113*10^296
N(074)= 1.1074982161*10^301
N(075)= 1.1702258575*10^306
N(076)= 1.2708236906*10^311
N(077)= 1.4178472793*10^316
N(078)= 1.6245983078*10^321
N(079)= 1.9110976601*10^326
N(080)= 2.3072358936*10^331
N(081)= 2.8577815955*10^336
N(082)= 3.6303902862*10^341
N(083)= 4.7285467047*10^346
N(084)= 6.3127465589*10^351
N(085)= 8.6356454899*10^356
N(086)= 1.2101233851*10^362
N(087)= 1.7365949825*10^367
N(088)= 2.5514087172*10^372
N(089)= 3.8366794584*10^377
N(090)= 5.9034935596*10^382
N(091)= 9.2923915625*10^387
N(092)= 1.4958912377*10^393
N(093)= 2.4621719380*10^398
N(094)= 4.1426351775*10^403
N(095)= 7.1231380487*10^408
N(096)= 1.2514140535*10^414
N(097)= 2.2457762023*10^419
N(098)= 4.1159546090*10^424
N(099)= 7.7022608903*10^429
N(100)= 1.4713509428*10^435
N(101)= 2.8686229449*10^440
N(102)= 5.7069018590*10^445
N(103)= 1.1582690665*10^451
N(104)= 2.3978098482*10^456
N(105)= 5.0621153989*10^461
N(106)= 1.0896293399*10^467
N(107)= 2.3909692644*10^472
N(108)= 5.3473450352*10^477
N(109)= 1.2186906566*10^483
N(110)= 2.8298493765*10^488
N(111)= 6.6937986357*10^493
N(112)= 1.6126783242*10^499
N(113)= 3.9565464637*10^504
N(114)= 9.8834176012*10^509
N(115)= 2.5133361679*10^515
N(116)= 6.5054600596*10^520
N(117)= 1.7136498552*10^526
N(118)= 4.5932132989*10^531
N(119)= 1.2525542396*10^537
N(120)= 3.4745449465*10^542
N(121)= 9.8029759472*10^547
N(122)= 2.8126438985*10^553
N(123)= 8.2055482735*10^558
N(124)= 2.4337543030*10^564
N(125)= 7.3377573424*10^569
N(126)= 2.2485865671*10^575
N(127)= 7.0025888888*10^580
N(128)= 2.2159216973*10^586
N(129)= 7.1242942351*10^591
N(130)= 2.3268409991*10^597
N(131)= 7.7192587782*10^602
N(132)= 2.6008539431*10^608
N(133)= 8.8988942258*10^613
N(134)= 3.0916112407*10^619
N(135)= 1.0904663541*10^625
N(136)= 3.9045301751*10^630
N(137)= 1.4190762004*10^636
N(138)= 5.2344986091*10^641
N(139)= 1.9594294230*10^647
N(140)= 7.4425667821*10^652
N(141)= 2.8681940015*10^658
N(142)= 1.1213513838*10^664
N(143)= 4.4471086086*10^669
N(144)= 1.7888444956*10^675
N(145)= 7.2976482890*10^680
N(146)= 3.0190201223*10^686
N(147)= 1.2664255737*10^692
N(148)= 5.3861984220*10^697
N(149)= 2.3223786646*10^703
N(150)= 1.0150589847*10^709