First numbers that belong to both sets:
1,
8,
64,
512,
2197,
4096,
12167,
15625,
17576,
24389,
32768,
42875,
79507,
91125,
97336,
117649,
125000,
132651,
140608,
195112,
205379,
226981,
262144,
300763,
328509,
343000,
357911,
389017,
456533,
493039,
614125,
636056,
704969,
729000,
778688,
804357,
857375,
912673,
941192,
970299,
1000000,
1030301,
1061208,
1092727,
1124864,
1295029,
1367631,
1442897,
1520875,
1560896,
1601613,
1643032,
1685159,
1815848,
1860867,
1953125,
2097152,
2248091,
2352637,
2406104,
2628072,
2685619,
2744000,
2863288,
3112136,
3307949,
3442951,
3581577,
3652264,
3723875,
3869893,
3944312,
4173281,
4330747,
4492125,
4657463,
4913000,
5000211,
5088448,
5177717,
5639752,
5735339,
5832000,
5929741,
6128487,
6229504,
6331625,
6434856,
6539203,
6751269,
6859000,
6967871,
7189057,
7301384,
7414875,
7529536,
7645373,
7762392,
7880599,
8000000,
8242408,
8489664,
8741816,
8869743,
8998912,
9393931,
9663597,
10360232,
10793861,
10941048,
11390625,
11543176,
12008989,
12167000,
12326391,
12487168,
12812904,
12977875,
13144256,
13481272,
13997521,
14348907,
14526784,
14886936,
15069223,
15438249,
15625000,
15813251,
16194277,
16777216,
17373979,
17779581,
17984728,
18821096,
19248832,
20346417,
20796875,
21024576,
21484952,
21952000,
22906304,
23149125,
24897088,
25153757,
26463592,
27270901,
27543608,
27818127,
28372625,
28652616,
29218112,
29791000,
30080231,
30664297,
30959144,
31255875,
31554496,
32461759,
33386248,
33698267,
34645976,
34965783,
35611289,
35937000,
36926037,
37259704,
38272753,
39304000,
40001688,
40353607,
40707584,
41421736,
43986977,
45118016,
45882712,
46656000,
47045881,
47437928,
47832147,
49027896,
49430863,
49836032,
50653000,
51478848,
52313624,
52734375,
53582633,
54010152,
54872000,
55742968,
56181887,
57066625,
57512456,
58411072,
58863869,
59319000,
60236288,
61162984,
61629875,
62099136,
62570773,
63044792,
64000000,
65939264,
67917312,
68417929,
69426531,
69934528,
70957944,
71473375,
71991296,
72511713,
73560059,
75151448,
77308776,
77854483,
78953589,
80062991,
82312875,
82881856,
84604519,
86350888,
86938307,
87528384,
91125000,
92345408,
94196375,
96071912,
96702579,
97336000,
97972181,
98611128,
99897344,
100544625,
101847563,
102503232,
103161709,
103823000,
105154048,
105823817,
107171875,
107850176,
109902239,
111980168,
114791256,
116214272,
119095488,
120553784,
121287375,
122763473,
123505992,
124251499,
125000000,
125751501,
126506008,
129554216,
130323843,
131872229,
134217728,
136590875,
138188413,
138991832,
141420761,
142236648,
143877824,
146363183,
148035889,
149721291,
150568768,
151419437,
153130375,
153990656,
154854153,
158340421,
160103007,
161878625,
162771336,
165469149,
166375000,
167284151.
Some larger examples :
860085351,
862801408,
870983875,
879217912,
887503681,
893056347,
895841344,
918330048,
929714176,
932574833,
949862087,
952763904,
955671625,
964430272,
967361669,
970299000,
982107784,
988047936,
994011992,
1000000000.