$\begin{array}{l}
{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)\\
27{x^3} + {y^3} = {\left( {3x} \right)^3} + {y^3} = \left( {3x + y} \right)\left( {9{x^2} - 3y + {y^2}} \right)\\
\Rightarrow \left( {27{x^3} + {y^3}} \right):\left( {9{x^2} - 3y + {y^2}} \right)\\
= \left( {3x + y} \right)\left( {9{x^2} - 3y + {y^2}} \right):\left( {9{x^2} - 3y + {y^2}} \right)\\
= 3x + y
\end{array}$
