First numbers that belong to both sets:
125,
128,
243,
256,
343,
512,
625,
729,
1024,
1331,
1369,
1681,
1849,
2048,
2187,
2197,
2209,
2401,
2809,
3125,
3481,
3721,
4096,
4489,
4913,
5041,
5329,
6241,
6561,
6859,
6889,
7921,
8192,
9409,
10000,
10125,
10201,
10368,
10609,
10976,
11449,
11664,
11881,
11907,
12167,
12500,
12544,
12769,
12800,
13824,
14641,
15552,
15625,
16000,
16129,
16384,
16807,
16875,
17161,
17496,
18225,
18769,
19208,
19321,
19683,
20000,
20736,
21609,
21952,
22201,
22801,
23328,
24389,
24649,
25000,
25088,
26244,
26569,
27783,
27889,
28125,
28561,
29791,
29929,
30375,
30625,
31104,
32000,
32041,
32761,
32768,
34992,
35721,
36481,
37249,
38416,
38809,
39601,
40000,
41472,
42875,
43904,
44521,
46656,
49729,
50000,
50625,
50653,
51529,
52441,
52488,
54289,
54675,
57121,
58081,
59049,
60025,
62208,
62500,
63001,
64000,
64827,
65536,
66049,
67228,
68921,
69169,
69984,
72361,
73441,
76729,
76832,
78125,
78732,
78961,
79507,
80000,
80089,
83349,
83521,
84375,
85849,
87808,
91125,
93312,
94249,
96721,
97969,
100000,
100352,
100467,
100489,
102400,
103823,
104976,
105125,
105625,
107163,
107584,
107648,
107653,
107811,
108241,
109503,
109561,
109744,
110224,
110592,
110889,
111392,
112225,
113569,
114244,
117128,
117649,
118336,
119072,
119164,
120125,
120409,
121203,
121801,
122825,
123008,
123201,
123823,
124416,
124609,
125000,
126025,
126736,
128000,
128547,
128881,
130321,
131072,
131769,
132651,
133225,
134456,
134689,
135424,
136107,
136161,
137641,
139129,
139968,
140608,
140625,
141376,
143641,
143648,
143883,
146689,
147456,
147968,
148877,
149769,
150544,
151263,
151321,
151875,
153125,
153664,
156025,
157216,
157464,
157609,
160000,
160801,
161051,
161312,
164025,
165888,
166375,
167281,
168507,
170368,
170528,
170569,
171125,
171475,
172225,
175232,
175561,
175616,
177147,
177241,
177957,
178929,
179776,
180625,
181447,
182329,
184832,
185193,
185761,
186003,
186624,
187489,
192721,
194481,
194672,
195112,
196249,
198025,
199712,
200000,
200704,
201601,
202612,
204363,
204800,
205379,
208849,
209952,
210125,
210681,
212521,
213867.
Some larger examples :
998496801,
998560000,
998623201,
998687432,
998812816,
998939236,
999002449,
999065664,
999128881,
999381769,
999389016,
999402632,
999406512,
999450207,
999508225,
999581472,
999634689,
999697924,
999761161,
999887641.