First numbers that belong to both sets:
25,
121,
125,
128,
216,
289,
343,
625,
1024,
1296,
2048,
2187,
2500,
2592,
2916,
3125,
3375,
4096,
4624,
5776,
5832,
8192,
9025,
9216,
9261,
10201,
10368,
11025,
11664,
12100,
12167,
12321,
12544,
12769,
12996,
13225,
13689,
13824,
14641,
15125,
15552,
15625,
16384,
16807,
16875,
17689,
18225,
18432,
19321,
19683,
19773,
20736,
21952,
23328,
24336,
24389,
24964,
25921,
26244,
26896,
27436,
27648,
27783,
27889,
28224,
28561,
28900,
29584,
29768,
29929,
30625,
32761,
32768,
34992,
35152,
35721,
35937,
36864,
37249,
38416,
39304,
41472,
42025,
42336,
42875,
43264,
45369,
46656,
48672,
51200,
52488,
53824,
54872,
55225,
55296,
59049,
59319,
65536,
67228,
68644,
69984,
70225,
73984,
76832,
78125,
78732,
81225,
82944,
83521,
84375,
84672,
85264,
91125,
93312,
97336,
99225,
103684,
103823,
103968,
104329,
104976,
105625,
106929,
107163,
107584,
107653,
108241,
111132,
112896,
114244,
114921,
117128,
117649,
118336,
119025,
121203,
123904,
124416,
124609,
125000,
125316,
126025,
126736,
127449,
128164,
129600,
130321,
131072,
131769,
132496,
132651,
133225,
133956,
134456,
134689,
135424,
136161,
137288,
137641,
139129,
139392,
139968,
140608,
140625,
141376,
142129,
142884,
143648,
143748,
145924,
146689,
147456,
148176,
148225,
151263,
151875,
152352,
153664,
157464,
159201,
161051,
162409,
163216,
164025,
165375,
165888,
166375,
167281,
169744,
170569,
171396,
172872,
175232,
175616,
176400,
177147,
177241,
178929,
180625,
181476,
183184,
184832,
185193,
186624,
187272,
188356,
189225,
191664,
192721,
194481,
194672,
195112,
195364,
196249,
198025,
202248,
204800,
205379,
207936,
209764,
209952,
210125,
210681,
214369,
214375,
215168,
215296,
216000,
216225,
217156,
218700,
219024,
219961,
221184,
221841,
222784,
223587,
223729,
224676,
224939,
225625,
225792,
226576,
226981,
227529,
228484,
228488,
228528,
231361,
231525,
232324,
233289,
233523,
233928,
234256,
235224,
235225,
236196,
236672,
237169,
237276,
238144,
238328,
238572,
239121,
239432,
241081,
242064,
243049,
243675,
244036,
247009,
248832,
249696,
250000,
250047,
251001,
252004,
253009,
253125.
Some larger examples :
938961,
941192,
944784,
946729,
950625,
952576,
953312,
954529,
962361,
963272,
966289,
968256,
968832,
969624,
970299,
972196,
978121,
990025,
992016,
995328.