Find $ \left(-18a+3\right)^3 $ in two steps.

S1: Swap two terms inside bracket

S2: apply formula

$$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$

where $ A = 3 $ and $ B = 18a $.

$$ \left(-18a+3\right)^3 \xlongequal{ S1 } \left(3-18a\right)^3 = 3^3-3 \cdot 3^2 \cdot 18a + 3 \cdot 3 \cdot \left( 18a \right)^2-\left( 18a \right)^3 = 27-486a+2916a^2-5832a^3 $$

Find $ \left(18a+3\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ 18a } $ and $ B = \color{red}{ 3 }$.

$$ \begin{aligned}\left(18a+3\right)^2 = \color{blue}{\left( 18a \right)^2} +2 \cdot 18a \cdot 3 + \color{red}{3^2} = 324a^2+108a+9\end{aligned} $$

Multiply $ \color{blue}{2} $ by $ \left( 27-486a+2916a^2-5832a^3\right) $ $$ \color{blue}{2} \cdot \left( 27-486a+2916a^2-5832a^3\right) = 54-972a+5832a^2-11664a^3 $$Multiply $ \color{blue}{6} $ by $ \left( 324a^2+108a+9\right) $ $$ \color{blue}{6} \cdot \left( 324a^2+108a+9\right) = 1944a^2+648a+54 $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( 1944a^2+648a+54 \right) = -1944a^2-648a-54 $$

Combine like terms:

$$ \, \color{blue}{ \cancel{54}} \, \color{green}{-972a} + \color{orange}{5832a^2} -11664a^3 \color{orange}{-1944a^2} \color{green}{-648a} \, \color{blue}{ -\cancel{54}} \, = -11664a^3+ \color{orange}{3888a^2} \color{green}{-1620a} $$