To simplify the expression \((y + 3z)(y^2 - 3yz + 9z^2) - 9z^3\), we can start by expanding the product \((y + 3z)(y^2 - 3yz + 9z^2)\) and then subtracting \(9z^3\).

First, let's expand \((y + 3z)(y^2 - 3yz + 9z^2)\):

\[
(y + 3z)(y^2 - 3yz + 9z^2) = y(y^2 - 3yz + 9z^2) + 3z(y^2 - 3yz + 9z^2)
\]

Now distribute \(y\) and \(3z\) to each term inside the parentheses:

\[
y(y^2 - 3yz + 9z^2) = y^3 - 3y^2z + 9yz^2
\]

\[
3z(y^2 - 3yz + 9z^2) = 3zy^2 - 9z^2y + 27z^3
\]

Combine these results:

\[
y^3 - 3y^2z + 9yz^2 + 3zy^2 - 9z^2y + 27z^3
\]

Now, combine like terms:

\[
y^3 + (-3y^2z + 3zy^2) + (9yz^2 - 9z^2y) + 27z^3
\]

\[
y^3 + 0y^2z + 0yz^2 + 27z^3
\]

\[
y^3 + 27z^3
\]

Now, subtract \(9z^3\):

\[
y^3 + 27z^3 - 9z^3
\]

Combine the \(z^3\) terms:

\[
y^3 + 18z^3
\]

So, the simplified expression is:

\[
y^3 + 18z^3
\]