First numbers that belong to both sets:
1,
27,
125,
343,
1331,
2197,
2744,
3375,
4913,
6859,
9261,
12167,
13824,
24389,
29791,
35937,
42875,
50653,
59319,
68921,
74088,
79507,
97336,
103823,
132651,
140608,
148877,
166375,
175616,
185193,
205379,
226981,
238328,
274625,
287496,
300763,
328509,
343000,
357911,
389017,
456533,
493039,
512000,
571787,
614125,
658503,
704969,
753571,
804357,
830584,
857375,
912673,
1030301,
1092727,
1157625,
1225043,
1295029,
1367631,
1442897,
1481544,
1520875,
1601613,
1685159,
1728000,
1860867,
2048383,
2146689,
2248091,
2352637,
2571353,
2628072,
2685619,
2803221,
2863288,
2924207,
3048625,
3307949,
3442951,
3511808,
3652264,
3723875,
3796416,
3869893,
3944312,
4019679,
4173281,
4330747,
4410944,
4492125,
4657463,
4741632,
5177717,
5545233,
5735339,
5929741,
6028568,
6128487,
6229504,
6331625,
6434856,
6539203,
6751269,
6967871,
7189057,
7414875,
7645373,
7880599,
8120601,
8365427,
8615125,
8741816,
9129329,
9261000,
9393931,
9663597,
9938375.