First numbers that belong to both sets:
1,
4,
8,
16,
36,
72,
243,
324,
400,
441,
800,
864,
1125,
1296,
1944,
2809,
2916,
3456,
3481,
3872,
4624,
4900,
5184,
6889,
7776,
8192,
10584,
11236,
11881,
13689,
14283,
15488,
17689,
18432,
19600,
19683,
20736,
21904,
24025,
25000,
25921,
29403,
34969,
36504,
39204,
45796,
47089,
47524,
47961,
56169,
59536,
65219,
72361,
73984,
75843,
78961,
84500,
84872,
87616,
88200,
95481,
97336,
99127,
102152,
106929,
114921,
120409,
123823,
127449,
141376,
147456,
154449,
160000,
163592,
172872,
175616,
177957,
184041,
190096,
196249,
197136,
197568,
203401,
210125,
224676,
242000,
253125,
253472,
272484,
274625,
292032,
293764,
295704,
303372,
304200,
311364,
313632,
323208,
338000,
342792,
346921,
349448,
350464,
352800,
356409,
376712,
379456,
383688,
385875,
386884,
390625,
391876,
392000,
393129,
400689,
405224,
405769,
412164,
419528,
451584,
455877,
460800,
469225,
484416,
484812,
493039,
501264,
504008,
521752,
527076,
553536,
574992,
575532,
585225,
592900,
609408,
616225,
620289,
625000,
634207,
663552,
665500,
672400,
680625,
682587,
685900,
692224,
702464,
704969,
708964,
712336,
765625,
779689,
781456,
788544,
793016,
864000,
874800,
884547,
912600,
940900,
950625,
964467,
975375,
984987,
985527,
996872,
1000000,
1010025,
1032256,
1058000,
1094116,
1104601,
1108809,
1114407,
1120581,
1147041,
1168561,
1182816,
1183744,
1194649,
1196836,
1203052,
1213488,
1218375,
1224963,
1279161,
1292832,
1299600,
1305728,
1318688,
1320201,
1364552,
1387684,
1397792,
1423656,
1444000,
1445000,
1454436,
1485172,
1488024,
1498176,
1512500,
1513800,
1516563,
1520768,
1527752,
1534752,
1540081,
1543500,
1547536,
1595169,
1602756,
1641672,
1672704,
1682209,
1687401,
1703025,
1711125,
1744712,
1752192,
1759688,
1769472,
1778112,
1812608,
1817104,
1830609,
1843200,
1893376,
1897352,
1898884,
1912689,
1934881,
1936000,
1946025,
1954404,
2025000,
2048288,
2105352,
2126696,
2131600,
2140369,
2154888,
2195200,
2196324,
2229049,
2247001,
2302128,
2328676,
2349675,
2413827,
2478175,
2481156,
2500000,
2505889,
2582449,
2596167,
2598544,
2598977,
2608328,
2621161,
2628288,
2640625,
2645163,
2653641,
2656192,
2661336,
2667168,
2669956,
2679769,
2695275,
2719201,
2725801,
2730348,
2768896,
2835856,
2856100,
2900209,
2941225,
2956824.
Some larger examples :
8946081,
9090225,
9162729,
9227808,
9273368,
9290304,
9363600,
9398700,
9443329,
9486400,
9504889,
9662408,
9687627,
9690769,
9720000,
9752427,
9759376,
9785888,
9796900,
9980928.