Natural numbers are arranged at regular intervals on the sides and vertices of squares with side lengths $1, 3, 5, \cdots, 2 n - 1, \cdots$ as shown in the figure below. In each square, 1 is placed directly above the lower left vertex. Let the $2 \times 2$ matrices with the natural numbers at the four vertices of each square as components be $A _ { 1 } , A _ { 2 } , A _ { 3 } , \cdots , A _ { n } , \cdots$ in order. For example, $A _ { 1 } = \left( \begin{array} { l l } 1 & 2 \\ 4 & 3 \end{array} \right) , A _ { 2 } = \left( \begin{array} { c c } 3 & 6 \\ 12 & 9 \end{array} \right)$. Find the sum of all components of matrix $A _ { 15 }$. [4 points]
Natural numbers are arranged at regular intervals on the sides and vertices of squares with side lengths $1, 3, 5, \cdots, 2 n - 1, \cdots$ as shown in the figure below. In each square, 1 is placed directly above the lower left vertex.
Let the $2 \times 2$ matrices with the natural numbers at the four vertices of each square as components be $A _ { 1 } , A _ { 2 } , A _ { 3 } , \cdots , A _ { n } , \cdots$ in order. For example, $A _ { 1 } = \left( \begin{array} { l l } 1 & 2 \\ 4 & 3 \end{array} \right) , A _ { 2 } = \left( \begin{array} { c c } 3 & 6 \\ 12 & 9 \end{array} \right)$.\\
Find the sum of all components of matrix $A _ { 15 }$. [4 points]