First numbers that belong to both sets:
25,
121,
289,
625,
1024,
1296,
2500,
2916,
4096,
4624,
5776,
9025,
9216,
10201,
11025,
11664,
12100,
12321,
12544,
12769,
12996,
13225,
13689,
14641,
15625,
16384,
17689,
18225,
19321,
20736,
24336,
24964,
25921,
26244,
26896,
27889,
28224,
28561,
28900,
29584,
29929,
30625,
32761,
35721,
36864,
37249,
38416,
42025,
43264,
45369,
46656,
53824,
55225,
59049,
65536,
68644,
70225,
73984,
81225,
82944,
83521,
85264,
99225,
103684,
104329,
104976,
105625,
106929,
107584,
108241,
112896,
114244,
114921,
117649,
118336,
119025,
123904,
124609,
125316,
126025,
126736,
127449,
128164,
129600,
130321,
131769,
132496,
133225,
133956,
134689,
135424,
136161,
137641,
139129,
140625,
141376,
142129,
142884,
145924,
146689,
147456,
148225,
153664,
159201,
162409,
163216,
164025,
167281,
169744,
170569,
171396,
176400,
177241,
178929,
180625,
181476,
183184,
186624,
188356,
189225,
192721,
194481,
195364,
196249,
198025,
207936,
209764,
210681,
214369,
215296,
216225,
217156,
219024,
219961,
221841,
222784,
223729,
224676,
225625,
226576,
227529,
228484,
231361,
232324,
233289,
234256,
235225,
236196,
237169,
238144,
239121,
241081,
242064,
243049,
244036,
247009,
250000,
251001,
252004,
253009,
254016,
255025,
256036,
257049,
258064,
259081,
262144,
263169,
264196,
265225,
267289,
268324,
269361,
271441,
272484,
273529,
274576,
275625,
278784,
279841,
281961,
283024,
285156,
286225,
287296,
288369,
290521,
291600,
292681,
293764,
294849,
295936,
297025,
298116,
314721,
319225,
320356,
321489,
322624,
327184,
328329,
329476,
331776,
334084,
338724,
342225,
345744,
346921,
351649,
352836,
354025,
355216,
361201,
362404,
363609,
366025,
367236,
376996,
378225,
379456,
381924,
385641,
388129,
389376,
390625,
391876,
393129,
398161,
401956,
412164,
414736,
416025,
417316,
419904,
426409,
427716,
432964,
436921,
442225,
446224,
454276,
455625,
456976,
458329,
462400,
465124,
467856,
469225,
470596,
471969,
474721,
478864,
487204,
495616,
497025,
511225,
512656,
521284,
522729,
524176,
525625,
527076,
531441,
532900,
535824,
537289,
570025,
571536,
577600,
579121,
582169,
585225,
586756,
589824,
597529,
602176,
614656,
616225,
627264,
632025.
Some larger examples :
919681,
921600,
923521,
925444,
927369,
931225,
937024,
938961,
944784,
946729,
950625,
952576,
954529,
962361,
966289,
968256,
972196,
978121,
990025,
992016.