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cubic n.  and  odious n.

First numbers that belong to both sets:

1, 8, 64, 512, 2197, 4096, 12167, 15625, 17576, 24389, 32768, 42875, 79507, 91125, 97336, 117649, 125000, 132651, 140608, 195112, 205379, 226981, 262144, 300763, 328509, 343000, 357911, 389017, 456533, 493039, 614125, 636056, 704969, 729000, 778688, 804357, 857375, 912673, 941192, 970299, 1000000, 1030301, 1061208, 1092727, 1124864, 1295029, 1367631, 1442897, 1520875, 1560896, 1601613, 1643032, 1685159, 1815848, 1860867, 1953125, 2097152, 2248091, 2352637, 2406104, 2628072, 2685619, 2744000, 2863288, 3112136, 3307949, 3442951, 3581577, 3652264, 3723875, 3869893, 3944312, 4173281, 4330747, 4492125, 4657463, 4913000, 5000211, 5088448, 5177717, 5639752, 5735339, 5832000, 5929741, 6128487, 6229504, 6331625, 6434856, 6539203, 6751269, 6859000, 6967871, 7189057, 7301384, 7414875, 7529536, 7645373, 7762392, 7880599, 8000000, 8242408, 8489664, 8741816, 8869743, 8998912, 9393931, 9663597, 10360232, 10793861, 10941048, 11390625, 11543176, 12008989, 12167000, 12326391, 12487168, 12812904, 12977875, 13144256, 13481272, 13997521, 14348907, 14526784, 14886936, 15069223, 15438249, 15625000, 15813251, 16194277, 16777216, 17373979, 17779581, 17984728, 18821096, 19248832, 20346417, 20796875, 21024576, 21484952, 21952000, 22906304, 23149125, 24897088, 25153757, 26463592, 27270901, 27543608, 27818127, 28372625, 28652616, 29218112, 29791000, 30080231, 30664297, 30959144, 31255875, 31554496, 32461759, 33386248, 33698267, 34645976, 34965783, 35611289, 35937000, 36926037, 37259704, 38272753, 39304000, 40001688, 40353607, 40707584, 41421736, 43986977, 45118016, 45882712, 46656000, 47045881, 47437928, 47832147, 49027896, 49430863, 49836032, 50653000, 51478848, 52313624, 52734375, 53582633, 54010152, 54872000, 55742968, 56181887, 57066625, 57512456, 58411072, 58863869, 59319000, 60236288, 61162984, 61629875, 62099136, 62570773, 63044792, 64000000, 65939264, 67917312, 68417929, 69426531, 69934528, 70957944, 71473375, 71991296, 72511713, 73560059, 75151448, 77308776, 77854483, 78953589, 80062991, 82312875, 82881856, 84604519, 86350888, 86938307, 87528384, 91125000, 92345408, 94196375, 96071912, 96702579, 97336000, 97972181, 98611128, 99897344, 100544625, 101847563, 102503232, 103161709, 103823000, 105154048, 105823817, 107171875, 107850176, 109902239, 111980168, 114791256, 116214272, 119095488, 120553784, 121287375, 122763473, 123505992, 124251499, 125000000, 125751501, 126506008, 129554216, 130323843, 131872229, 134217728, 136590875, 138188413, 138991832, 141420761, 142236648, 143877824, 146363183, 148035889, 149721291, 150568768, 151419437, 153130375, 153990656, 154854153, 158340421, 160103007, 161878625, 162771336, 165469149, 166375000, 167284151.

Some larger examples :