First numbers that belong to both sets:
1,
8,
64,
125,
216,
512,
729,
1000,
1728,
2197,
2744,
4096,
4913,
5832,
8000,
9261,
10648,
13824,
15625,
17576,
21952,
24389,
27000,
32768,
35937,
39304,
46656,
50653,
54872,
64000,
68921,
74088,
85184,
91125,
97336,
110592,
117649,
125000,
140608,
148877,
157464,
175616,
185193,
195112,
216000,
226981,
238328,
262144,
274625,
287496,
314432,
328509,
343000,
373248,
389017,
405224,
438976,
456533,
474552,
512000,
531441,
551368,
592704,
614125,
636056,
681472,
704969,
729000,
778688,
804357,
830584,
884736,
912673,
941192,
1000000,
1030301,
1061208,
1124864,
1157625,
1191016,
1259712,
1295029,
1331000,
1404928,
1442897,
1481544,
1560896,
1601613,
1643032,
1728000,
1771561,
1815848,
1906624,
1953125,
2000376,
2097152,
2146689,
2197000,
2299968,
2352637,
2406104,
2515456,
2571353,
2628072,
2744000,
2803221,
2863288,
2985984,
3048625,
3112136,
3241792,
3307949,
3375000,
3511808,
3581577,
3652264,
3796416,
3869893,
3944312,
4096000,
4173281,
4251528,
4410944,
4492125,
4574296,
4741632,
4826809,
4913000,
5088448,
5177717,
5268024,
5451776,
5545233,
5639752,
5832000,
5929741,
6028568,
6229504,
6331625,
6434856,
6644672,
6751269,
6859000,
7077888,
7189057,
7301384,
7529536,
7645373,
7762392,
8000000,
8120601,
8242408,
8489664,
8615125,
8741816,
8998912,
9129329,
9261000,
9528128,
9663597,
9800344,
10077696,
10218313,
10360232,
10648000,
10793861,
10941048,
11239424,
11390625,
11543176,
11852352,
12008989,
12167000,
12487168,
12649337,
12812904,
13144256,
13312053,
13481272,
13824000,
13997521,
14172488,
14526784,
14706125,
14886936,
15252992,
15438249,
15625000,
16003008,
16194277,
16387064,
16777216,
16974593,
17173512,
17576000,
17779581,
17984728,
18399744,
18609625,
18821096,
19248832,
19465109,
19683000,
20123648,
20346417,
20570824,
21024576,
21253933,
21484952,
21952000,
22188041,
22425768,
22906304,
23149125,
23393656,
23887872,
24137569,
24389000,
24897088,
25153757,
25412184,
25934336,
26198073,
26463592,
27000000,
27270901,
27543608,
28094464,
28372625,
28652616,
29218112,
29503629,
29791000,
30371328,
30664297,
30959144,
31554496,
31855013,
32157432,
32768000,
33076161,
33386248,
34012224,
34328125,
34645976,
35287552,
35611289,
35937000,
36594368,
36926037,
37259704,
37933056,
38272753,
38614472,
39304000,
39651821,
40001688,
40707584,
41063625,
41421736,
42144192,
42508549,
42875000,
43614208,
43986977,
44361864,
45118016,
45499293,
45882712,
46656000,
47045881,
47437928,
48228544,
48627125,
49027896,
49836032,
50243409,
50653000,
51478848,
51895117.
Some larger examples :
924010424,
929714176,
932574833,
935441352,
941192000,
944076141,
946966168,
952763904,
955671625,
958585256,
964430272,
967361669,
970299000,
976191488,
979146657,
982107784,
988047936,
991026973,
994011992,
1000000000.