Difference between Two Squares equal to Repdigit

Theorem
Some differences of two squares that each make a repdigit number include:

Proof
Let $a, b$ be integers with $1 \le b < a \le 8$ and $a + b = 9$.

Then:

which is a repdigit number.

The examples above are instances with $\tuple {a, b} = \tuple {5, 4}, \tuple {6, 3}, \tuple {7, 2}, \tuple {8, 1}$.