\begin{tabular}{|l|c|c|c|c|c|c|c|c|} \hline $\mathrm{x}$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline $\mathrm{f}(\mathrm{x})$ & 3 & 2 & 1 & -2 & 3 & 4 & 0 & 5 \\ \hline $\mathrm{f}^{\prime}(\mathrm{x})$ & -2 & -1 & 2 & 4 & 1 & 0 & 3 & 6 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|c|c|c|c|c|c|} \hline $\mathrm{x}$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline $\mathrm{g}(\mathrm{x})$ & 1 & 3 & 5 & 2 & -1 & 0 & -2 & 4 \\ \hline $\mathrm{g}^{\prime}(\mathrm{x})$ & 2 & 3 & -2 & 0 & -3 & 4 & 1 & 5 \\ \hline \end{tabular} Enter your answer as a whole number (like 6 or 3 or -9 ) \[ \text { When } x=6 \text { then }\left(x^{3}+f(x)\right)^{\prime}= \]

Step 1 ：The derivative of a function is a measure of how a function changes as its input changes. In this case, we are asked to find the derivative of the function \(x^{3}+f(x)\) at \(x=6\).

Step 2 ：The derivative of a sum of functions is the sum of the derivatives of the functions. So, we need to find the derivative of \(x^{3}\) and the derivative of \(f(x)\), and then add them together.

Step 3 ：The derivative of \(x^{3}\) is \(3x^{2}\).

Step 4 ：The derivative of \(f(x)\) is given in the table as \(f'(x)\).

Step 5 ：So, the derivative of \(x^{3}+f(x)\) is \(3x^{2}+f'(x)\).

Step 6 ：We are asked to find the value of this derivative at \(x=6\).

Step 7 ：Substitute \(x=6\) and \(f'(x)=3\) into the derivative expression, we get \(3*6^{2}+3=111\).

Step 8 ：Final Answer: The derivative of the function \(x^{3}+f(x)\) at \(x=6\) is \(\boxed{111}\).