1. The problem is to understand how to perform the third difference of squares. 2. The difference of squares formula is $a^2 - b^2 = (a-b)(a+b)$. 3. The "third difference" usually means applying the difference operation three times in sequence. 4. Let's consider a sequence of squares: $1^2, 2^2, 3^2, 4^2, 5^2, \ldots$ which is $1, 4, 9, 16, 25, \ldots$. 5. The first difference is the difference between consecutive terms: $4-1=3$, $9-4=5$, $16-9=7$, $25-16=9$, so the first difference sequence is $3, 5, 7, 9, \ldots$. 6. The second difference is the difference of the first difference sequence: $5-3=2$, $7-5=2$, $9-7=2$, so the second difference sequence is $2, 2, 2, \ldots$. 7. The third difference is the difference of the second difference sequence: $2-2=0$, $2-2=0$, so the third difference sequence is $0, 0, \ldots$. 8. This shows that the third difference of squares is zero because the sequence of squares is a quadratic sequence, and the third difference of a quadratic sequence is always zero. 9. In summary, the third difference of squares is $0$.