There is no a that will make f(x) continuous.
No matter what value of a you pick, you will always have the one-sided limits,
[tex]\displaystyle \lim_{x\to a^-}f(x) = \lim_{x\to a}(x^2-a^2) = 0[/tex]
[tex]\displaystyle \lim_{x\to a^+}f(x) = \lim_{x\to a}(x^2-a^2) = 0[/tex]
but f(a) = 8 regardless of a.
