\[
f(x)=7 x^{3}+6 x^{2}+x
\]
Step 2 of 2 : Evaluate $f^{\prime \prime}(1), f^{\prime \prime}(8)$, and $f^{\prime \prime}(0)$, if they exist. If they do not exist, select "Does Not Exist".

Step 1 ：Given the function \(f(x)=7 x^{3}+6 x^{2}+x\), we need to find the second derivatives at \(x = 1\), \(x = 8\), and \(x = 0\).

Step 2 ：First, we find the first derivative of \(f(x)\). The derivative of a constant times a function is the constant times the derivative of the function. The derivative of \(x^n\) is \(n*x^{n-1}\). So, the first derivative of \(f(x)\) is \(f'(x) = 21x^2 + 12x + 1\).

Step 3 ：Then, we find the second derivative of \(f(x)\). The second derivative gives us the rate of change of the rate of change, or how the slope of the function is changing. The second derivative of \(f(x)\) is \(f''(x) = 42x + 12\).

Step 4 ：We then substitute \(x = 1\), \(x = 8\), and \(x = 0\) into \(f''(x)\) to find \(f''(1)\), \(f''(8)\), and \(f''(0)\).

Step 5 ：The second derivatives of the function at \(x = 1\), \(x = 8\), and \(x = 0\) are \(f''(1) = 54\), \(f''(8) = 348\), and \(f''(0) = 12\).

Step 6 ：So, the final answers are \(f''(1) = \boxed{54}\), \(f''(8) = \boxed{348}\), and \(f''(0) = \boxed{12}\).