First numbers that belong to both sets:
125,
216,
343,
2197,
2744,
3375,
8000,
9261,
10648,
12167,
13824,
21952,
24389,
27000,
29791,
39304,
50653,
54872,
59319,
68921,
91125,
97336,
103823,
140608,
148877,
157464,
166375,
175616,
216000,
226981,
238328,
250047,
274625,
328509,
343000,
357911,
456533,
474552,
493039,
512000,
592704,
614125,
636056,
658503,
681472,
778688,
804357,
830584,
857375,
884736,
1030301,
1061208,
1092727,
1295029,
1331000,
1367631,
1404928,
1560896,
1601613,
1643032,
1685159,
1728000,
1906624,
1953125,
2000376,
2048383,
2352637,
2406104,
2460375,
2515456,
2571353,
2628072,
2803221,
2863288,
2924207,
3048625,
3241792,
3307949,
3375000,
3442951,
3511808,
3652264,
3796416,
3869893,
3944312,
4019679,
4173281,
4410944,
4492125,
4574296,
4657463,
5177717,
5268024,
5359375,
5832000,
5929741,
6028568,
6128487,
6229504,
6644672,
6751269,
6859000,
6967871,
7301384,
7645373,
7762392,
7880599,
8615125,
8741816,
8869743,
8998912,
9261000,
9528128,
9663597,
9800344,
9938375.