First numbers that belong to both sets:
216,
441,
1521,
2601,
4356,
8192,
8649,
9261,
11025,
19881,
25281,
29241,
31329,
35937,
36864,
41209,
44100,
59319,
66564,
68121,
68921,
69696,
82944,
84681,
91809,
95481,
97344,
99225,
103684,
110592,
142884,
152100,
154449,
159201,
161051,
164025,
168921,
169744,
171396,
181476,
185193,
194481,
199809,
213444,
216000,
216225,
219024,
236196,
238328,
242064,
248832,
250047,
251001,
260100,
269361,
275625,
281961,
285156,
288369,
294849,
301401,
308025,
311364,
314432,
318096,
328509,
338724,
349281,
352836,
357911,
367236,
378225,
389376,
435600,
451584,
480249,
505521,
524288,
527076,
535824,
540225,
549081,
553536,
571787,
580644,
589824,
592704,
609961,
622521,
627264,
632025,
658503,
660969,
720801,
725904,
731025,
736164,
759375,
788544,
793881,
799236,
804357,
831744,
842724,
864900,
870489,
887364,
956484,
962361.