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odious n.  and  taxicab n.

First numbers that belong to both sets:

1729, 13832, 20683, 40033, 65728, 110656, 134379, 149389, 165464, 195841, 320264, 443889, 525824, 593047, 704977, 805688, 885248, 984067, 994688, 1009736, 1016496, 1075032, 1092728, 1195112, 1323712, 1331064, 1533357, 1566728, 1609272, 1774656, 1845649, 2048391, 2418271, 2562112, 2691451, 2991816, 3375001, 3375008, 3511872, 3551112, 3587409, 3628233, 4206592, 4511808, 4607064, 4673088, 4744376, 4931101, 5004125, 5135104, 5446359, 5462424, 5639816, 5832729, 6013000, 6058747, 6445504, 6517000, 7081984, 7094269, 7872536, 7882245, 7957504, 8077888, 8131968, 8216000, 8600256, 8741824, 8872487, 9016488, 9443761, 9560896, 10424232, 10469816, 10589696, 10648512, 10765603, 10821896, 10870119, 11097567, 11859211, 11985003, 12266856, 12533824, 12650337, 12874176, 13489875, 13851000, 14197248, 14482503, 14765192, 14916727, 15438250, 16012269, 16387128, 16387189, 16587207, 16776487, 16983854, 17999072, 18406603, 19346168, 20162952, 20496896, 20616463, 21531608, 21753576, 21994875, 22754277, 23934528, 24480125, 24767171, 24897817, 25164405, 25371171, 25785432, 26506467, 27000008, 27000064, 27015625, 27445392, 28094976, 28408896, 28658448, 28699272, 28703269, 29025864, 29184057, 29503656, 29791125, 32114143, 33652736, 35938728, 36094464, 36856512, 37384704, 37498032, 37955008, 39448808, 40033000, 40134584, 40354119, 40519115, 40970375, 41080832, 41258737, 41511232, 43450344, 43570872, 43699392, 43852536, 43946000, 45118528, 45440551, 45882739, 46661832, 47915712, 48104000, 48469976, 49832523, 49933368, 51240427, 51564032, 52136000, 52242463, 52739288, 53226297, 54814509, 54887625, 55486125, 56655872, 56754152, 58751784, 59913728, 60271939, 61555832, 62108397, 62980288, 63057960, 63660032, 64421875, 64623104, 65055744, 65293317, 65573928, 65728000, 66469429, 68007673, 68802048, 69583995, 69625969, 69805125, 69934592, 70449093, 70957971, 70979896, 71292312, 72131904, 73819863, 74097261, 74130875, 75550088, 76487168, 77414967, 79692193, 80779032, 83393856, 83758528, 84266000, 84637287, 84717568, 85188096, 85492792, 85502375, 86124824, 86368464, 86575168, 86960952, 87029432, 87539319, 88780536, 89576767, 90527229, 91034307, 91125027, 91125216, 91140435, 94100426, 94873688, 95731489, 95880024, 96860043, 97867441, 97962291, 98040969, 98134848, 99768753, 100270592, 101202696, 101615579, 102993408, 106496767, 107919000, 108904581, 110087432, 110808000, 111485673, 111906333, 112422709, 113577984, 115084125, 115860024, 115942104, 116215603, 118121536, 118974960, 119082880, 119333816, 119377000, 119793457, 121660623, 122810129, 123262120, 123506000, 124336000, 126173376, 126516061, 126906624, 128098152, 131097024, 131097512, 131126303, 131997229, 132697656, 134171875, 134211896, 135111375, 135870832, 137467603, 141117704.

Some larger examples :