What is the value of $3\cdot 3 + 3(3 + 3) - 3^3$?
Applying the order of operations gives \begin{align*}
3\cdot 3 +3(3+3) - 3^3 &= 3\cdot 3 +3(6) - 3^3\\
&= 3\cdot 3 + 3(6) - 27\\
&= 9 + 18 - 27 = \boxed{0}.
\end{align*}