First numbers that belong to both sets:
4,
8,
9,
36,
100,
144,
196,
216,
225,
324,
400,
441,
484,
576,
676,
784,
900,
1089,
1156,
1444,
1521,
1764,
1936,
2116,
2601,
2704,
3025,
3249,
3364,
3600,
3844,
4225,
4356,
4624,
4761,
4900,
5476,
5776,
5929,
6084,
6724,
7056,
7225,
7396,
7569,
7744,
8100,
8281,
8464,
8649,
8836,
9025,
9216,
9801,
10404,
11025,
12100,
12996,
14400,
15876,
16900,
17424,
19044,
19600,
20449,
22500,
23716,
24336,
27000,
27225,
28224,
28900,
30276,
32400,
33124,
34596,
34969,
36100,
38025,
39204,
40804,
41616,
42436,
43681,
44100,
45796,
47524,
48400,
48841,
49284,
51076,
51984,
52900,
53361,
54756,
56644,
57600,
60516,
61009,
63504,
64009,
64516,
65025,
66564,
67600,
68644,
69696,
70756,
72900,
74088,
74529,
75076,
76176,
77284,
78400,
79524,
81225,
81796,
84100,
86436,
88804,
89401,
90000,
91204,
91809,
93636,
94864,
95481,
96100,
97344,
98596,
99225,
101124,
103684,
108900,
115600,
116964,
119025,
121104,
125316,
127449,
132496,
133956,
136900,
138384,
139876,
144400,
148225,
152100,
156816,
159201,
161604,
164836,
166464,
168100,
171396,
174724,
176400,
181476,
184041,
184900,
188356,
189225,
191844,
193600,
195364,
197136,
207025,
207936,
211600,
213444,
216225,
219024,
220900,
224676,
226576,
230400,
233289,
242064,
244036,
245025,
248004,
256036,
260100,
266256,
268324,
270400,
272484,
278784,
280900,
283024,
285156,
287496,
298116,
302500,
304704,
308025,
311364,
314721,
318096,
324900,
327184,
329476,
336400,
338724,
342225,
348100,
352836,
354025,
357604,
362404,
367236,
370881,
372100,
374544,
378225,
379456,
381924,
384400,
389376,
393129,
396900,
404496,
407044,
412164,
414736,
416025,
417316,
422500,
423801,
427716,
432964,
435600,
439569,
442225,
443556,
448900,
451584,
459684,
462400,
465124,
467856,
474552,
476100,
480249,
484416,
492804,
497025,
501264,
504100,
509796,
511225,
527076,
529984,
532900,
535824,
544644,
547600,
549081,
550564,
553536,
559504,
568516,
576081,
577600,
580644,
585225,
592900,
599076,
603729,
608400,
611524,
617796,
624100,
627264,
632025,
636804,
646416,
648025,
649636.
Some larger examples :
9696996,
9709456,
9734400,
9746884,
9759376,
9771876,
9784384,
9790641,
9796900,
9828225,
9847044,
9859600,
9884736,
9891025,
9897316,
9922500,
9947716,
9960336,
9966649,
9998244.