First numbers that belong to both sets:
25,
121,
127,
289,
625,
1255,
1296,
1395,
1435,
1792,
2187,
2500,
2503,
2504,
2507,
2509,
2592,
3159,
3685,
4106,
4167,
4624,
5120,
5776,
6144,
6145,
9025,
9216,
10192,
10251,
10368,
10426,
10525,
10824,
11259,
11264,
11665,
12100,
12104,
12288,
12337,
12493,
12505,
12544,
12550,
12595,
12769,
12843,
12960,
13125,
13496,
13764,
13822,
13825,
13826,
13832,
14175,
14641,
15379,
15568,
15613,
15621,
15622,
15625,
15626,
15628,
15633,
15634,
15656,
15679,
15688,
16245,
16295,
16348,
16372,
16375,
16381,
16382,
16385,
16387,
16447,
16448,
16479,
16743,
16758,
16783,
16797,
16798,
16807,
17253,
17368,
17384,
17482,
17536,
17856,
17892,
17920,
17925,
18225,
18432,
18594,
19453,
19592,
19653,
19682,
19684,
19734,
19737,
19738,
19845,
20736,
21375,
21495,
21504,
21606,
21844,
21848,
21953,
22528,
23392,
23456,
23546,
23548,
24336,
24367,
24375,
24564,
24576,
24584,
24964,
25105,
25314,
25872,
26624,
26754,
26896,
28226,
28559,
28672,
28678,
28749,
28764,
28900,
29282,
29584,
29632,
31250,
31252,
31256,
32744,
32747,
32761,
32762,
32764,
32771,
32772,
32778,
32783,
32785,
32786,
32795,
32825,
32832,
32836,
32845,
32851,
32853,
32854,
33579,
33696,
34968,
34992,
35152,
35684,
35721,
35932,
35942,
36864,
37249,
37840,
38416,
38912,
39295,
39313,
39314,
39362,
39368,
39456,
41472,
42875,
43268,
43688,
44676,
45056,
45361,
45362,
45364,
45368,
45632,
45864,
45947,
46256,
46626,
46632,
46640,
46655,
46657,
46658,
46660,
46664,
46672,
46688,
47652,
48672,
48750,
48755,
48757,
48758,
49152,
49896,
51200,
51398,
52483,
52498,
53245,
53248,
53824,
54369,
54436,
55225,
57644,
59039,
59055,
59129,
59263,
59318,
59375,
59759,
62476,
62504,
62968,
63478,
63895,
63985,
64513,
65480,
65483,
65485,
65486,
65488,
65491,
65528,
65542,
65841,
67149,
67228,
67252,
67392,
68644,
68800,
69253,
69472,
69984,
69993,
73984,
74353,
74533,
76832,
76835,
78115,
78117,
78132,
78136,
78225,
78975,
81920,
82755,
82942,
82944,
83957.
Some larger examples :
976595,
976625,
977589,
978128,
979769,
980092,
981225,
982560,
983041,
983042,
983044,
983047,
983048,
983485,
984375,
986947,
990025,
995336,
995344,
997375.