First numbers that belong to both sets:
4,
8,
9,
16,
25,
27,
32,
36,
49,
64,
81,
100,
121,
125,
128,
144,
169,
225,
243,
256,
289,
324,
343,
361,
392,
400,
484,
512,
529,
576,
625,
676,
729,
784,
800,
841,
900,
961,
968,
1024,
1089,
1156,
1225,
1296,
1331,
1352,
1369,
1444,
1600,
1681,
1849,
1936,
2025,
2048,
2116,
2187,
2197,
2209,
2304,
2312,
2401,
2500,
2601,
2704,
2809,
2888,
2916,
3025,
3087,
3125,
3136,
3267,
3364,
3481,
3600,
3721,
3844,
3872,
4096,
4225,
4232,
4356,
4489,
4624,
4761,
4913,
5041,
5184,
5329,
5408,
5476,
5625,
5776,
6075,
6125,
6241,
6272,
6400,
6561,
6724,
6728,
6859,
6889,
7225,
7396,
7569,
7688,
7744,
7803,
7921,
8100,
8192,
8281,
8464,
8836,
9025,
9216,
9248,
9261,
9409,
10000,
10201,
10404,
10609,
10816,
10952,
11236,
11449,
11552,
11664,
11881,
12100,
12167,
12769,
12800,
13225,
13448,
13456,
13924,
14161,
14283,
14400,
14641,
14792,
14884,
15125,
15129,
15488,
15625,
16129,
16384,
16807,
16900,
16928,
17161,
17424,
17672,
17956,
18225,
18496,
18769,
19044,
19208,
19321,
19600,
19683,
19881,
20000,
20164,
20449,
20736,
21025,
21316,
21609,
21632,
21904,
22201,
22472,
22500,
22707,
22801,
23104,
23409,
24389,
24649,
24964,
25088,
25281,
25600,
26244,
26569,
26896,
26912,
27225,
27556,
27783,
27848,
27889,
28561,
28900,
29403,
29584,
29768,
29791,
29929,
30276,
30625,
30752,
30976,
31329,
31684,
32041,
32400,
32761,
32768,
33275,
33856,
34225,
34969,
35344,
35912,
36100,
36125,
36481,
36864,
37249,
37636,
38416,
38809,
39601,
40000,
40328,
40804,
41209,
41616,
42025,
42436,
42632,
42849,
43264,
43808,
44521,
44944,
45125,
45369,
45387,
45796,
46208,
46225,
46656,
47089,
47524,
48400,
48841,
49729,
49928,
50176,
50625,
50653,
51076,
51529,
52441,
52900,
53792,
53824,
54289,
55112,
55225,
55696,
57121,
57600,
57967,
58081,
58564,
59049,
59168,
59319,
59536,
59643,
60025.
Some larger examples :
9872164,
9874568,
9878449,
9884736,
9891025,
9892352,
9897316,
9903609,
9909904,
9916201,
9927968,
9928801,
9935104,
9954025,
9960336,
9972964,
9981512,
9985600,
9991921,
9999392.