First numbers that belong to both sets:
1000,
1331,
1728,
8000,
24389,
27000,
39304,
110592,
125000,
175616,
216000,
250047,
274625,
314432,
421875,
512000,
592704,
970299,
1000000,
1061208,
1157625,
1259712,
1331000,
1560896,
1601613,
1728000,
1771561,
2197000,
2460375,
2744000,
2985984,
3241792,
3375000,
3511808,
3796416,
4096000,
4492125,
4741632,
4913000,
5268024,
5832000,
6229504,
7414875,
7762392,
8000000,
9261000,
10077696,
10648000,
10941048,
11239424,
11390625,
11852352,
12167000,
12326391,
13144256,
13824000,
15069223,
15625000,
16003008,
16581375,
16777216,
17173512,
17576000,
19683000,
20346417,
20796875,
21952000,
23149125,
23393656,
24389000,
25412184,
25672375,
27000000,
27818127,
28372625,
29218112,
29791000,
31255875,
35287552,
35937000,
36926037,
37933056,
39651821,
41063625,
42875000,
46656000,
50653000,
54872000,
56623104,
57066625,
59319000,
62099136,
65939264,
74088000,
85184000,
85766121,
91125000,
94818816,
98611128,
100544625,
102503232,
103823000,
107850176,
110592000,
117649000,
119095488,
119823157,
121287375,
122023936,
123505992,
125000000,
128024064,
130323843,
132651000,
137388096,
140608000,
142236648,
144703125,
147197952,
148877000,
153990656,
157464000,
166375000,
168196608,
170953875,
171879616,
173741112,
175616000,
176558481,
185193000,
189119224,
191102976,
195112000,
197137368,
200201625,
205379000,
209584584,
210644875,
216000000,
218167208,
219256227,
221445125,
225866529,
226981000,
232608375,
238328000,
242970624,
244140625,
250047000,
253636137,
256047875,
259694072,
262144000,
268336125,
274625000,
275894451,
279726264,
281011375,
287496000,
291434247,
294079625,
296740963,
325660672,
328509000,
337153536,
347428927,
354894912,
363994344,
373248000,
376367048,
382657176,
385828352,
397065375,
405224000,
420189749,
421875000,
438976000,
447697125,
456533000,
474552000,
493039000,
496793088,
512000000,
519718464,
531441000,
535387328,
551368000,
561515625,
563559976,
571787000,
580093704,
592704000,
601211584,
603351125,
644972544,
653972032,
658503000,
690807104,
700227072,
753571000,
766060875,
773620632,
817400375,
830584000,
846590536,
884736000,
970299000,
988047936,
1000000000,
1003003001,
1006012008,
1009027027,
1015075125,
1024192512,
1030301000,
1048772096,
1061208000,
1083206683,
1092727000,
1099104768,
1108717875,
1111934656,
1118386872,
1124864000,
1157625000,
1177583616,
1191016000,
1197770328,
1204550144,
1207949625,
1218186432,
1225043000,
1245766976,
1259712000,
1295029000,
1302170688,
1312932375,
1316532736,
1323753192,
1331000000,
1367631000,
1371330631,
1389928896,
1404928000,
1412467848,
1423828125,
1435249152,
1442897000,
1458274104,
1466003456,
1481544000,
1520875000,
1528823808,
1540798875,
1544804416,
1548816893,
1552836312,
1556862679,
1560896000,
1601613000,
1613964717,
1626379776,
1643032000,
1651400568,
1664006625,
1676676672,
1685159000,
1710777536,
1728000000,
1745337664,
1771561000,
1780360128,
1793613375,
1798045696,
1806932232,
1815848000,
1820316861,
1860867000,
1888232256,
1906624000.
Some larger examples :
85184000000,
85242093201,
86350888000,
86468159448,
86820610752,
87528384000,
88716536000,
89915392000,
91125000000,
91611864512,
92468044648,
92959677000,
93329542656,
94631796693,
94818816000,
96702579000,
96829042688,
97082300736,
98611128000,
99961946721.