First numbers that belong to both sets:
9,
49,
108,
169,
216,
225,
500,
625,
675,
676,
841,
961,
968,
2744,
2916,
3087,
3125,
3249,
3267,
3528,
3721,
3888,
3969,
4000,
7225,
8649,
10609,
11881,
11907,
11979,
12100,
12168,
12321,
12769,
13924,
14641,
14792,
15625,
16129,
16875,
17689,
22707,
27783,
29241,
32400,
36125,
38025,
39601,
40500,
41209,
41503,
42849,
44944,
45369,
45387,
45796,
47524,
52900,
54000,
54872,
55112,
56644,
58081,
60500,
60516,
61731,
62001,
64009,
64800,
65025,
128547,
133100,
136107,
137200,
151321,
154449,
154568,
155236,
156025,
158184,
160083,
161604,
163216,
163592,
167281,
168507,
176868,
177241,
177608,
180000,
181447,
182408,
183184,
185761,
187272,
187489,
189225,
191664,
192721,
194672,
195075,
195112,
198916,
199712,
207576,
209764,
212552,
217156,
218700,
219024,
219700,
220448,
223112,
225000,
228484,
228488,
231361,
232324,
236196,
236672,
239432,
240737,
244036,
245000,
247009,
247808,
250000,
252004,
253472,
254043,
255025,
256328,
259081,
260876,
261121,
264600,
276768,
288000,
288800,
289000,
295936,
300304,
302500,
304704,
311904,
314721,
315844,
316368,
326432,
336400,
338688,
345744,
364816,
366368,
372100,
383688,
384400,
386884,
396508,
401956,
412164,
414736,
419528,
432000,
438012,
441800,
446224,
453152,
456300,
463736,
480200,
490000,
496008,
531441,
533871,
544500,
561001,
571787,
583443,
596183,
609961,
613089,
613832,
615627,
622521,
630436,
632025,
636804,
644204,
649636,
653400,
660969,
665500,
667489,
674041,
675684,
677329,
684500,
686792,
687241,
696200,
701784,
702244,
707281,
711828,
712336,
714025,
715208,
717409,
724201,
727609,
731025,
740772,
741125,
744012,
744769,
748225,
751689,
751896,
767376,
768800,
771147,
773768,
777600,
781456,
784000,
810448,
817452,
820125,
829921,
830584,
837225,
840500,
850084,
855468,
857500,
861125,
877969,
882000,
885481,
894348,
898704,
902500,
904203,
908552,
910116,
914112,
924500,
927472,
933156,
940896,
946729,
953312,
960400,
963272,
972000,
980100,
986049,
996004,
998784,
1012036,
1016172,
1018081,
1028196,
1028376,
1034289,
1042441,
1042568,
1046529,
2074464,
2105352,
2112500,
2131947,
2145125,
2171528,
2196608,
2208492,
2211169,
2221832,
2222316.
Some larger examples :
198810000,
198894609,
199043848,
199120968,
199204996,
199317924,
199430884,
199459129,
199480536,
199520288,
199628388,
199656900,
199692000,
199712000,
199713424,
199756800,
199809000,
199895904,
199939600,
199967881.