\[x^{2} + mx + 27 = 0;\ \ x_{1} = 3x_{2}.\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = - m \\ x_{1} \cdot x_{2} = 27\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ }\]
\[3x_{2} \cdot x_{2} = 27\]
\[3x_{2}^{2} = 27\]
\[x_{2}^{2} = 9\]
\[x_{2} = \pm 3.\]
\[x_{1} = 3 \cdot ( \pm 3) \Longrightarrow \ \ x_{1} = \pm 9.\]
\[9 + 3 = - m\]
\[12 = - m \Longrightarrow m = - 12.\]
\[- 9 - 3 = - m\ \ \]
\[- 12 = - m \Longrightarrow m = 12.\]
\[Ответ:9;\ 3;\ - 12\ \ или\ \ - 9;\ \]
\[- 3;12.\]