First numbers that belong to both sets:
64,
81,
324,
1024,
2500,
5184,
9604,
15625,
16384,
26244,
40000,
58564,
59049,
82944,
114244,
153664,
202500,
262144,
331776,
334084,
419904,
521284,
640000,
777924,
937024,
1048576,
1119364,
1265625,
1327104,
1562500,
1827904,
2125764,
2359296,
2458624,
2829124,
3240000,
3694084,
3779136,
4194304,
4743684,
5345344,
5764801,
6002500,
6718464,
7496644,
8340544,
9253764,
9529569,
10240000,
11303044,
12446784,
13675204,
14992384,
16000000,
16402500,
17909824,
19518724,
21233664,
23059204,
25000000,
27060804,
29246464,
31561924,
34012224,
36602500,
39337984,
42224004,
43046721,
45265984,
48469444,
51840000,
55383364,
59105344,
63011844,
67108864,
71402500,
75898944,
80604484,
81000000,
85525504,
90668484,
96040000,
101646724,
107495424,
113592964,
119946304,
126562500,
133448704,
140612164,
143496441,
148060224,
155800324,
163840000,
172186884,
180848704,
189833284,
199148544,
208802500,
218803264,
229159044,
239878144,
241864704,
250968964,
262440000,
274299844,
286557184,
299220804,
312299584,
325802500,
339738624,
354117124,
368947264,
384238404,
390971529,
400000000,
416241604,
432972864,
450203524,
467943424,
486202500,
504990784,
524318404,
544195584,
564632644,
585640000,
607228164,
609892416,
629407744,
652189444,
675584064,
688747536,
699602500,
724255744,
749554884,
775511104,
802135684,
829440000,
857435524,
886133824,
915546564,
922640625,
945685504,
976562500,
1008189504,
1040578564,
1073741824,
1107691524,
1142440000,
1177999684,
1214383104,
1251602884,
1289671744,
1328602500,
1358954496,
1368408064,
1409101444,
1450695744,
1493204164,
1536640000,
1581016644,
1626347584,
1672646404,
1719926784,
1768202500,
1817487424,
1867795524,
1919140864,
1955143089,
1971537604,
2025000000,
2079542404,
2135179264,
2191925124,
2249794624,
2308802500,
2368963584,
2430292804,
2492805184,
2556515844,
2621440000,
2687592964,
2754990144,
2823647044,
2893579264,
2964802500,
3037332544,
3111185284,
3186376704,
3262922884,
3340840000,
3420144324,
3486784401,
3500852224,
3582980164,
3666544704,
3751562500,
3810716361,
3838050304,
3926024964,
4015503424,
4106502724,
4199040000,
4293132484,
4388797504,
4486052484,
4584914944,
4685402500,
4787532864,
4891323844,
4996793344,
5103959364,
5184000000,
5212840000,
5323453444,
5435817984,
5549952004,
5665873984,
5783602500,
5903156224,
6024553924,
6147814464,
6272956804,
6400000000,
6528963204,
6659865664,
6792726724,
6927565824,
6947055801,
7064402500,
7203256384,
7344147204,
7487094784,
7632119044,
7779240000,
7928477764,
8079852544,
8233384644,
8389094464,
8547002500,
8707129344,
8869495684,
9034122304,
9183772224,
9201030084,
9370240000,
9541773124,
9715650624,
9891893764,
10070523904,
10251562500,
10435031104,
10620951364,
10809345024,
11000233924,
11193640000,
11389585284,
11588091904,
11789182084,
11990907009,
11992878144,
12199202500,
12408177664,
12619826244,
12834170944,
13051234564,
13271040000,
13493610244,
13718968384,
13947137604,
14178141184,
14412002500,
14648745024,
14888392324,
15130968064,
15376496004,
15479341056,
15625000000,
15876504004,
16131032064,
16384000000.
Some larger examples :
9426385938564,
9456855040000,
9487397946244,
9518014776384,
9529569000000,
9548705649604,
9579470685184,
9610310002500,
9641223721024,
9672211960324,
9703274840064,
9734412480004,
9765625000000,
9796912520004,
9828275160064,
9859713040324,
9891226281024,
9922815002500,
9954479325184,
9986219369604.