\[\boxed{\mathbf{13}.}\]
\[1)\ 2^{3} - 2^{0} - 2^{- 3} + ( - 2)^{3} +\]
\[+ ( - 2)^{- 3} = 8 - 1 - \frac{1}{8} - 8 -\]
\[- \frac{1}{8} = - 1\frac{2}{8} = - 1\frac{1}{4}\]
\[2)\ \frac{3^{- 3} \cdot 3^{5}}{3^{3}} + \left( 3^{- 1} \right)^{2} - \left( \frac{3^{2}}{3^{3}} \right)^{2} =\]
\[= \frac{1}{3} + \frac{1}{9} - \left( \frac{1}{3} \right)^{2} = \frac{1}{3} + \frac{1}{9} - \frac{1}{9} = \frac{1}{3}\]