Step 1 :Consider the function \(f(x)=\frac{x^{2}-64}{x-8}\).
Step 2 :We need to find the x-values where the denominator of the function, which is \(x-8\), is zero.
Step 3 :Solving the equation \(x-8=0\), we find that \(x=8\).
Step 4 :Therefore, the function is not differentiable at \(x=8\).
Step 5 :Final Answer: The function is not differentiable at \(x=\boxed{8}\).