\[\begin{array}{l}
A = \left( {5a - 3b} \right)\left( {5a + 3b} \right) = 25{a^2} - 9{b^2}\\
\Rightarrow {A^3} = {\left( {25{a^2} - 9{b^2}} \right)^3} = {\left( {25{a^2}} \right)^3} - 3.{\left( {25{a^2}} \right)^2}.9{b^2} + 3.25{a^2}.{\left( {9{b^2}} \right)^2} - {\left( {9{b^2}} \right)^3}\\
= {25^3}{a^6} - {3.25^2}.{a^4}.9{b^2} + 3.25{a^2}{.9^2}{b^4} - {9^3}{b^6}\\
= {5^6}{a^6} - {3.5^4}.{a^4}{b^2}{.3^2} + {3.5^2}{a^2}{.3^4}.{b^4} - {3^9}.{b^6}\\
= {\left( {5a} \right)^6} - {3^3}{.5^4}{a^4}{b^2} + {3^5}{.5^2}{a^2}{b^4} - {3^9}.{b^6}.
\end{array}\]
