First numbers that belong to both sets:
216,
2744,
15625,
54872,
195112,
531441,
571787,
830584,
2248091,
2406104,
2744000,
2863288,
3581577,
3723875,
3869893,
7414875,
8615125,
8998912,
9129329,
9261000,
14706125,
16003008,
35611289,
36926037,
39304000,
45882712,
47437928,
49027896,
49430863,
52313624,
52734375,
53582633,
55742968,
58863869,
61162984,
62099136,
62570773,
65939264,
139798359,
140608000,
143055667,
155720872,
156590819,
159220088,
175616000,
179406144,
187149248.