First numbers that belong to both sets:
625,
729,
1369,
1681,
1849,
2209,
2401,
2809,
3481,
3721,
4489,
5041,
5329,
6241,
6561,
6889,
7921,
9409,
10201,
10609,
11449,
11881,
12769,
14641,
15625,
16129,
17161,
18225,
18769,
19321,
21609,
22201,
22801,
24649,
26569,
27889,
28561,
29929,
30625,
32041,
32761,
35721,
36481,
37249,
38809,
39601,
44521,
49729,
50625,
51529,
52441,
54289,
57121,
58081,
59049,
60025,
63001,
66049,
69169,
72361,
73441,
76729,
78961,
80089,
83521,
85849,
94249,
96721,
97969,
100489,
105625,
108241,
109561,
110889,
112225,
113569,
117649,
120409,
121801,
123201,
124609,
126025,
128881,
130321,
131769,
133225,
134689,
136161,
137641,
139129,
140625,
143641,
146689,
149769,
151321,
156025,
157609,
160801,
164025,
167281,
170569,
172225,
175561,
177241,
178929,
180625,
182329,
185761,
187489,
192721,
194481,
196249,
198025,
201601,
208849,
210681,
212521,
214369,
218089,
219961,
225625,
227529,
229441,
235225,
237169,
241081,
247009,
249001,
253009,
257049,
259081,
261121,
263169,
271441,
273529,
279841,
281961,
290521,
292681,
299209,
301401,
305809,
310249,
316969,
321489,
323761,
326041,
330625,
332929,
337561,
344569,
351649,
358801,
361201,
363609,
366025,
368449,
375769,
380689,
383161,
385641,
388129,
390625,
398161,
405769,
408321,
410881,
413449,
418609,
426409,
431649,
434281,
436921,
452929,
455625,
458329,
461041,
466489,
477481,
491401,
502681,
505521,
516961,
525625,
528529,
531441,
537289,
546121,
552049,
558009,
564001,
573049,
579121,
591361,
597529,
600625,
613089,
619369,
635209,
641601,
654481,
657721,
674041,
677329,
683929,
687241,
693889,
700569,
703921,
707281,
714025,
717409,
727609,
734449,
737881,
744769,
751689,
762129,
765625,
769129,
776161,
779689,
786769,
793881,
822649,
829921,
844561,
855625,
863041,
866761,
877969,
885481,
896809,
908209,
923521,
935089,
942841,
954529,
966289,
982081,
994009,
998001,
1006009,
1014049,
1018081,
1022121,
1026169,
1034289,
1038361,
1042441,
1050625,
1054729,
1058841,
1062961,
1067089,
1075369,
1079521,
1083681,
1087849,
1096209,
1100401,
1104601,
1108809,
1113025,
1117249,
1121481,
1125721,
1129969,
1138489,
1142761,
1151329,
1155625,
1159929,
1164241,
1168561,
1172889,
1181569,
1185921,
1190281,
1194649.
Some larger examples :
996980625,
997233241,
997359561,
997485889,
997612225,
997738569,
997864921,
997991281,
998117649,
998244025,
998370409,
998496801,
998623201,
999002449,
999128881,
999381769,
999508225,
999634689,
999761161,
999887641.