Magic Square Center Term
Algebra · proposed by @Cheesedog
A magic square is an array of integers (not necessarily distinct) arranged in a square grid such that the sum of every row, column, and both main diagonals is identical.
For a $3×3$ magic square, let $S$ be the sum of all 9 terms in the square, and let $\vartheta(S)$ be the set of all possible values for the center of the magic square. Find the sum of $$\sum_{S=1}^{2026} \sum_{c \in \vartheta(S)}c$$