First numbers that belong to both sets:
1,
4,
27,
72,
100,
121,
144,
200,
243,
324,
343,
400,
441,
1000,
1024,
1323,
1372,
1444,
2000,
2304,
2312,
2401,
2700,
2704,
2744,
3200,
3721,
4000,
7200,
7744,
10000,
10201,
10404,
12100,
12321,
14112,
14400,
17424,
20000,
22201,
22472,
22707,
23104,
24200,
24300,
27000,
40000,
40401,
41472,
43200,
44100,
44217,
70227,
70304,
72000,
72200,
73441,
100000,
101124,
102400,
103041,
110224,
114244,
121000,
121104,
121203,
123201,
144000,
144400,
174724,
177147,
177241,
200000,
200704,
203401,
204304,
223112,
240100,
242000,
243000,
270000,
270400,
271441,
274400,
300304,
301401,
303372,
304200,
304704,
310472,
314721,
320000,
324000,
343000,
372100,
373321,
400000,
407044,
421201,
423200,
441000,
473344,
474721,
477144,
702244,
707472,
720000,
722000,
724201,
740772,
741321,
743044,
744012,
744200,
771147,
774400.