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cubic n.  and  evil n.

First numbers that belong to both sets:

27, 125, 216, 343, 729, 1000, 1331, 1728, 2744, 3375, 4913, 5832, 6859, 8000, 9261, 10648, 13824, 19683, 21952, 27000, 29791, 35937, 39304, 46656, 50653, 54872, 59319, 64000, 68921, 74088, 85184, 103823, 110592, 148877, 157464, 166375, 175616, 185193, 216000, 238328, 250047, 274625, 287496, 314432, 373248, 405224, 421875, 438976, 474552, 512000, 531441, 551368, 571787, 592704, 658503, 681472, 753571, 830584, 884736, 1157625, 1191016, 1225043, 1259712, 1331000, 1404928, 1481544, 1728000, 1771561, 1906624, 2000376, 2048383, 2146689, 2197000, 2299968, 2460375, 2515456, 2571353, 2803221, 2924207, 2985984, 3048625, 3176523, 3241792, 3375000, 3511808, 3796416, 4019679, 4096000, 4251528, 4410944, 4574296, 4741632, 4826809, 5268024, 5359375, 5451776, 5545233, 6028568, 6644672, 7077888, 8120601, 8365427, 8615125, 9129329, 9261000, 9528128, 9800344, 9938375, 10077696, 10218313, 10503459, 10648000, 11089567, 11239424, 11697083, 11852352, 12649337, 13312053, 13651919, 13824000, 14172488, 14706125, 15252992, 16003008, 16387064, 16581375, 16974593, 17173512, 17576000, 18191447, 18399744, 18609625, 19034163, 19465109, 19683000, 19902511, 20123648, 20570824, 21253933, 21717639, 22188041, 22425768, 22665187, 23393656, 23639903, 23887872, 24137569, 24389000, 24642171, 25412184, 25672375, 25934336, 26198073, 26730899, 27000000, 28094464, 28934443, 29503629, 30371328, 31855013, 32157432, 32768000, 33076161, 34012224, 34328125, 35287552, 36264691, 36594368, 37595375, 37933056, 38614472, 38958219, 39651821, 41063625, 41781923, 42144192, 42508549, 42875000, 43243551, 43614208, 44361864, 44738875, 45499293, 46268279, 48228544, 48627125, 50243409, 51064811, 51895117, 53157376, 54439939, 55306341, 56623104, 57960603, 59776471, 60698457, 63521199, 64481201, 64964808, 65450827, 66430125, 66923416, 67419143, 68921000, 70444997, 73034632, 74088000, 74618461, 75686967, 76225024, 76765625, 78402752, 79507000, 80621568, 81182737, 81746504, 83453453, 84027672, 85184000, 85766121, 88121125, 88716536, 89314623, 89915392, 90518849, 91733851, 92959677, 93576664, 94818816, 95443993, 99252847, 101194696, 104487111, 106496424, 108531333, 109215352, 110592000, 111284641, 112678587, 113379904, 114084125, 115501303, 116930169, 117649000, 118370771, 119823157, 122023936, 127263527, 128024064, 128787625, 131096512, 132651000, 133432831, 135005697, 135796744, 137388096, 139798359, 140608000, 143055667, 144703125, 145531576, 147197952, 148877000, 152273304, 155720872, 156590819, 157464000, 159220088, 160989184, 163667323, 164566592, 170031464, 172808693, 173741112, 174676879, 176558481, 177504328, 179406144, 180362125, 181321496.

Some larger examples :