First numbers that belong to both sets:
561,
1105,
1729,
2465,
2821,
6601,
8911,
10585,
15841,
29341,
41041,
46657,
52633,
62745,
63973,
75361,
101101,
115921,
126217,
162401,
172081,
188461,
252601,
278545,
294409,
314821,
334153,
340561,
399001,
410041,
449065,
488881,
512461,
530881,
552721,
656601,
658801,
670033,
748657,
825265,
838201,
852841,
997633,
1024651,
1033669,
1050985,
1082809,
1152271,
1193221,
1461241,
1569457,
1615681,
1773289,
1857241,
1909001,
2100901,
2113921,
2433601,
2455921,
2508013,
2531845,
2628073,
2704801,
3057601,
3146221,
3224065,
3581761,
3664585,
3828001,
4335241,
4463641,
4767841,
4903921,
4909177,
5031181,
5049001,
5148001,
5310721,
5444489,
5481451,
5632705,
5968873,
6049681,
6054985,
6189121,
6313681,
6733693,
6840001,
6868261,
7207201,
7519441,
7995169,
8134561,
8341201,
8355841,
8719309,
8719921,
8830801,
8927101,
9439201,
9494101,
9582145,
9585541,
9613297,
9890881.