First numbers that belong to both sets:
1029,
1215,
1875,
3645,
4096,
10000,
10112,
10125,
10752,
10976,
11125,
11421,
12167,
13122,
13824,
13851,
14375,
14641,
14823,
15625,
17405,
18750,
20224,
21141,
21627,
22201,
24057,
24576,
24832,
25625,
27889,
28431,
28561,
32000,
34445,
38125,
38637,
40817,
40960,
41472,
46875,
48223,
54289,
59049,
71875,
73441,
74431,
76729,
83521,
100000,
101120,
101125,
101250,
101251,
102303,
102625,
102912,
103247,
103499,
103518,
103933,
104375,
104615,
104704,
105625,
105705,
106097,
107375,
107875,
107911,
108135,
108241,
108578,
109760,
109952,
110125,
110446,
110464,
111005,
111250,
111392,
111537,
112023,
112995,
113024,
113375,
113408,
113627,
114453,
115943,
116125,
116162,
117632,
118016,
118459,
118803,
120625,
120787,
120832,
121014,
121203,
121670,
121984,
122317,
122713,
123125,
123201,
123823,
124625,
125056,
126025,
126603,
131220,
131726,
132921,
133125,
134375,
134456,
135351,
135625,
136171,
137216,
137543,
137677,
137728,
139523,
140211,
140625,
143641,
143750,
145664,
146071,
146176,
146410,
148519,
149504,
150625,
152635,
154007,
155648,
156025,
156250,
157323,
157609,
159375,
159607,
160181,
160623,
161875,
162867,
163296,
164025,
167041,
170569,
171315,
173563,
178929,
179456,
180075,
180625,
180989,
182979,
184064,
185761,
186517,
187500,
187648,
190269,
190333,
191051,
192000,
194045,
195167,
196249,
197173,
197559,
197589,
198125,
201341,
201447,
202240,
202612,
204085,
205057,
205578,
205625,
207104,
210176,
210625,
212139,
212317,
212629,
214083,
214326,
218489,
218491,
219488,
220549,
220672,
223074,
225536,
226981,
227529,
229709,
230121,
230839,
231125,
231822,
232192,
232211,
233227,
234256,
235264,
236196,
237917,
240267,
240813,
241081,
241664,
245248,
245673,
245760,
248320,
249856,
250047,
250625,
253125,
253265,
254043,
256250,
257593,
257762,
259375,
263125,
263169,
264191,
265625,
266511,
267543,
268912,
269941,
271875,
278173,
280000,
280625,
282123,
283581,
284375,
285610,
288463,
288923,
292681,
293077,
297472,
299008,
300763,
303616,
304175,
308367,
310784,
311101,
314375,
314411,
315625,
317057,
317115,
320000,
320031,
324405,
325625,
329315,
332929,
337561,
339913,
339968,
340603,
341446,
347648,
351122,
352256.
Some larger examples :
9863185,
9865682,
9875000,
9878159,
9880115,
9884321,
9890625,
9891072,
9899323,
9901250,
9911957,
9918531,
9933354,
9936917,
9938999,
9945088,
9953125,
9990299,
9999803,
10000000.