First numbers that belong to both sets:
1,
27,
64,
1000,
1728,
2744,
3375,
5832,
8000,
9261,
10648,
17576,
35937,
39304,
54872,
59319,
85184,
97336,
216000,
343000,
592704,
729000,
1061208,
1331000,
1481544,
2197000,
2299968,
2628072,
3652264,
3796416,
4492125,
4913000,
5268024,
6028568,
6434856,
6859000,
7414875,
7762392,
8489664.