Problem #WSP-000363

Problem

After Albert discovered the previous rule, he began looking at differences of squares of consecutive odd numbers. He found the difference between $1^2$ and $3^2$ is $8$, the difference between $3^2$ and $5^2$ is $16$, the difference between $5^2$ and $7^2$ is $24$, and that the difference between $7^2$ and $9^2$ is $32$. What is the rule now? Can you prove it?