Sums of both 2 and 3 Consecutive Squares

Theorem
The following are the smallest positive integers that are the sum of both $2$ and $3$ consecutive non-zero square numbers:
 * $365, 35 \, 645, 3 \, 492 \, 725, 342 \, 251 \, 285, 33 \, 537 \, 133 \, 085, 3 \, 286 \, 296 \, 790 \, 925, \ldots$