First numbers that belong to both sets:
1,
1000,
4096,
12167,
13824,
15625,
74088,
226981,
250047,
300763,
531441,
704969,
778688,
1000000,
1092727,
1481544,
2460375,
2803221,
3176523,
3652264,
4096000,
4251528,
5000211,
6644672,
7645373,
8365427,
8489664,
8869743,
8998912.