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 :
938313739,
941192000,
944076141,
946966168,
949862087,
952763904,
955671625,
958585256,
961504803,
964430272,
967361669,
973242271,
976191488,
979146657,
982107784,
985074875,
988047936,
991026973,
994011992,
997002999.