\[\frac{(a - 2b)^{3}}{(2a - b)^{3}}\ :\frac{a^{2} - 4ab + 4b^{2}}{4a^{2} - 4ab + b^{2}} =\]
\[= \frac{(a - 2b)^{3}(2a - b)^{2}}{(2a - b)^{3}(a - 2b)^{2}} = \frac{a - 2b}{2a - b}.\]