First numbers that belong to both sets:
121,
729,
10201,
36481,
51529,
100489,
124609,
184041,
410881,
674041,
896809,
966289,
1038361,
1190281,
1238769,
1852321,
2975625,
3613801,
3892729,
4330561,
4809249,
4888521,
5031049,
5461569,
5527201,
5978025,
6517809,
6630625,
7059649,
7273809,
7868025,
7946761,
8048569,
8567329,
9150625,
9455625,
9678321,
10478169,
10569001,
11042329,
11553201,
12709225,
12909649,
13417569,
14922769,
15342889,
16654561,
21836929,
22496049,
23941449,
25371369,
25512601,
26842761,
27783441,
29084449,
32684089,
33605209,
34987225,
40386025,
41486481,
43072969,
47872561,
51739249,
52229529,
55487601,
55965361,
56505289,
56565441,
57108249,
57441241,
58415449,
58905625,
61199329,
62964225,
65173329,
65853225,
66373609,
67551961,
67881121,
68442529,
68740681,
69006249,
71622369,
71825625,
72505225,
76475025,
77704225,
78765625,
78907689,
79227801,
80299521,
84143929,
84548025,
84805681,
85137529,
86136961,
86955625,
87216921,
87815641,
93799225,
96530625.