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centered octagonal n.  and  junction n.

First numbers that belong to both sets:

2025, 5625, 7225, 10609, 11025, 18225, 19321, 21609, 23409, 24025, 27225, 30625, 34225, 35721, 38025, 41209, 42025, 44521, 50625, 57121, 60025, 61009, 65025, 68121, 70225, 81225, 87025, 93025, 114921, 119025, 120409, 130321, 133225, 140625, 148225, 156025, 164025, 178929, 180625, 192721, 205209, 216225, 225625, 239121, 245025, 255025, 265225, 273529, 277729, 308025, 314721, 319225, 332929, 342225, 354025, 366025, 403225, 408321, 416025, 429025, 469225, 483025, 505521, 511225, 540225, 555025, 570025, 616225, 622521, 632025, 677329, 703921, 714025, 731025, 741321, 748225, 769129, 790321, 851929, 859329, 874225, 912025, 923521, 931225, 954529, 1006009, 1010025, 1054729, 1071225, 1092025, 1113025, 1134225, 1159929, 1221025, 1234321, 1288225, 1311025, 1334025, 1375929, 1390041, 1404225, 1428025, 1452025, 1525225, 1535121, 1600225, 1630729, 1651225, 1661521, 1677025, 1703025, 1729225, 1760929, 1852321, 1879641, 1885129, 1896129, 1918225, 1974025, 2024929, 2030625, 2111209, 2117025, 2134521, 2146225, 2169729, 2175625, 2181529, 2205225, 2217121, 2235025, 2241009, 2265025, 2418025, 2449225, 2468041, 2486929, 2544025, 2706025, 2739025, 2805625, 2819041, 3045025, 3150625, 3157729, 3330625, 3337929, 3367225, 3404025, 3441025, 3463321, 3508129, 3705625, 3713329, 3783025, 3822025, 3884841, 3892729, 3908529, 4012009, 4020025, 4044121, 4100625, 4182025, 4223025, 4297329, 4431025, 4498641, 4507129, 4515625, 4601025, 4721929, 4818025, 4906225, 4941729, 4968441, 5040025, 5130225, 5166529, 5184729, 5313025, 5340721, 5414929, 5640625, 5650129, 5659641, 5736025, 5870929, 5890329, 5900041, 6027025, 6076225, 6175225, 6225025, 6305121, 6365529, 6385729, 6395841, 6528025, 6610041, 6620329, 6630625, 6640929, 6869641, 6880129, 6901129, 7144929, 7166329, 7177041, 7230721, 7414729, 7436529, 7480225, 7502121, 7590025, 7623121, 7711729, 7879249, 7958041, 8094025, 8151025, 8277129, 8543929, 8567329, 8579041, 8614225, 8862529, 8874441, 8958049, 9030025, 9150625, 9162729, 9174841, 9211225, 9259849, 9443329, 9703225, 9753129, 9790641, 10017225, 10067929, 10080625, 10208025, 10272025, 10336225, 10400625, 10530025, 10634121, 10660225, 10699441, 10725625, 10857025, 10923025, 11068929, 11122225, 11256025, 11458225, 11526025, 11716929, 11758041, 11937025, 12006225, 12061729, 12075625, 12089529, 12145225, 12173121, 12215025, 12524521, 12567025, 12709225, 12766329, 13039321, 13140625, 13242321, 13359025, 13402921, 13432225, 13801225, 13845841.

Some larger examples :