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cubic n.  and  frugal n.

First numbers that belong to both sets:

125, 343, 512, 729, 1331, 2197, 4096, 4913, 6859, 12167, 13824, 15625, 19683, 21952, 24389, 29791, 32768, 42875, 46656, 50653, 64000, 68921, 79507, 91125, 103823, 110592, 117649, 125000, 132651, 140608, 148877, 157464, 166375, 175616, 185193, 195112, 205379, 226981, 238328, 250047, 262144, 274625, 300763, 314432, 328509, 357911, 373248, 389017, 405224, 421875, 438976, 456533, 493039, 512000, 531441, 551368, 571787, 614125, 636056, 658503, 681472, 704969, 753571, 778688, 804357, 830584, 857375, 884736, 912673, 941192, 970299, 1000000, 1030301, 1092727, 1124864, 1157625, 1191016, 1225043, 1259712, 1295029, 1367631, 1404928, 1442897, 1520875, 1560896, 1601613, 1643032, 1685159, 1728000, 1771561, 1815848, 1860867, 1906624, 1953125, 2000376, 2048383, 2097152, 2146689, 2248091, 2352637, 2406104, 2460375, 2515456, 2571353, 2685619, 2744000, 2803221, 2863288, 2924207, 2985984, 3048625, 3112136, 3176523, 3241792, 3307949, 3375000, 3442951, 3511808, 3581577, 3723875, 3869893, 3944312, 4019679, 4096000, 4173281, 4251528, 4330747, 4410944, 4574296, 4657463, 4741632, 4826809, 5000211, 5088448, 5177717, 5359375, 5451776, 5545233, 5639752, 5735339, 5832000, 5929741, 6128487, 6229504, 6331625, 6539203, 6644672, 6751269, 6967871, 7077888, 7189057, 7301384, 7529536, 7645373, 7880599, 8000000, 8120601, 8242408, 8365427, 8615125, 8741816, 8869743, 8998912, 9129329, 9393931, 9528128, 9663597, 9800344, 9938375, 10077696, 10218313, 10360232, 10503459, 10648000, 10793861, 10941048, 11089567, 11239424, 11390625, 11543176, 11697083, 11852352, 12008989, 12167000, 12326391, 12487168, 12649337, 12812904, 12977875, 13144256, 13312053, 13481272, 13651919, 13824000, 13997521, 14172488, 14348907, 14526784, 14706125, 14886936, 15069223, 15252992, 15438249, 15625000, 15813251, 16003008, 16194277, 16387064, 16581375, 16777216, 16974593, 17173512, 17373979, 17576000, 17779581, 17984728, 18191447, 18399744, 18609625, 18821096, 19034163, 19248832, 19465109, 19683000, 19902511, 20123648, 20346417, 20570824, 20796875, 21024576, 21253933, 21484952, 21717639, 21952000, 22188041, 22425768, 22665187, 22906304, 23149125, 23639903, 23887872, 24137569, 24389000, 24642171, 24897088, 25153757, 25412184, 25672375, 25934336, 26198073, 26463592, 26730899, 27000000, 27270901, 27543608, 27818127, 28094464, 28372625, 28652616, 28934443, 29218112, 29503629, 29791000, 30080231, 30371328, 30664297, 30959144, 31255875, 31554496, 31855013, 32157432, 32461759, 32768000, 33076161, 33386248, 33698267, 34012224, 34328125, 34645976, 34965783.

Some larger examples :