\[\boxed{\mathbf{2.}\mathbf{182}}\]
\[n = 3:\]
\[\frac{3^{\backslash 3}}{14} - \frac{1^{\backslash 14}}{3} = \frac{9}{42} - \frac{14}{42} = - \frac{5}{42}.\]
\[n = 6:\]
\[\frac{6^{\backslash 3}}{14} - \frac{1^{\backslash 7}}{6} = \frac{18}{42} - \frac{7}{42} = \frac{11}{42}.\]
\[n = 7:\]
\[\frac{7}{14} - \frac{1^{\backslash 2}}{7} = \frac{7}{14} - \frac{2}{14} = \frac{1}{14}.\]