\[\left( 1\frac{1}{3} \right)^{3} = \left( \frac{3 + 1}{3} \right)^{3} = \left( \frac{4}{3} \right)^{3} =\]
\[= \frac{4^{3}}{3^{3}} = \frac{64}{27} = 2\frac{10}{27}\]