First numbers that belong to both sets:
25,
121,
125,
128,
153,
216,
289,
625,
688,
736,
1024,
1260,
1285,
1296,
1792,
2048,
2349,
2500,
2501,
2504,
2505,
2508,
2509,
2592,
2737,
2916,
3125,
3281,
3685,
3784,
3864,
3972,
4088,
4096,
4536,
4624,
4628,
5120,
5776,
5832,
6144,
6145,
6880,
7928,
8092,
8192,
9025,
9216,
9261,
10192,
10201,
10368,
10521,
10525,
10824,
11025,
11264,
11664,
11665,
11844,
11848,
12060,
12100,
12101,
12104,
12105,
12108,
12109,
12288,
12321,
12337,
12384,
12493,
12505,
12544,
12600,
12768,
12769,
12960,
12964,
12996,
13125,
13176,
13225,
13496,
13545,
13689,
13725,
13764,
13813,
13824,
13825,
13832,
14129,
14168,
14256,
14352,
14641,
14645,
15125,
15300,
15345,
15552,
15568,
15585,
15612,
15613,
15617,
15620,
15621,
15624,
15625,
15628,
15629,
15632,
15633,
15641,
15645,
15656,
15661,
15688,
15689,
15697,
16225,
16245,
16272,
16348,
16368,
16372,
16377,
16381,
16384,
16385,
16448,
16765,
16797,
17253,
17325,
17328,
17368,
17384,
17428,
17437,
17488,
17536,
17689,
17856,
17892,
17920,
17925,
18225,
18265,
18432,
18744,
19321,
19392,
19453,
19592,
19629,
19653,
19684,
19692,
19693,
19732,
19736,
19737,
19773,
19845,
20485,
20736,
21504,
21753,
21844,
21845,
21848,
21952,
21953,
22264,
22528,
22757,
23328,
23392,
23456,
23548,
23552,
23796,
24336,
24385,
24389,
24393,
24564,
24576,
24584,
24768,
24964,
24972,
25105,
25137,
25725,
25872,
25921,
26244,
26348,
26364,
26496,
26624,
26896,
26973,
27436,
27648,
27653,
27889,
28217,
28224,
28476,
28556,
28561,
28564,
28672,
28728,
28749,
28764,
28784,
28900,
29160,
29184,
29517,
29524,
29525,
29529,
29549,
29584,
29632,
29768,
29929,
30625,
31252,
31256,
31509,
32685,
32697,
32744,
32761,
32764,
32765,
32768,
32772,
32781,
32785,
32805,
32825,
32832,
32836,
32845,
32849,
32853,
32865,
32885,
33696,
34425,
34968,
34992,
34993,
34996,
35152,
35684,
35721,
35928,
35932,
35933,
35937,
36457,
36549,
36864,
37249,
37449,
37668,
37840,
37845,
38416.
Some larger examples :
983048,
983049,
983445,
983485,
983664,
983752,
985768,
987264,
990025,
992016,
992256,
995328,
995333,
995336,
995337,
995341,
995344,
995364,
995373,
999964.