a)$\begin{array}{l} {a^6} - {b^3}\\ = {\left( {{a^2}} \right)^3} - {b^3}\\ = \left( {{a^2} - b} \right)\left( {{a^4} + {a^2}b + {b^2}} \right) \end{array}$
b)
$\begin{array}{l} {x^4} - {y^4}\\ = \left( {{x^2} - {y^2}} \right)\left( {{x^2} + {y^2}} \right)\\ = \left( {x - y} \right)\left( {x + y} \right)\left( {{x^2} + {y^2}} \right) \end{array}$
c)
$\begin{array}{l} {\left( {\dfrac{x}{3} - 6y} \right)^3} = \dfrac{{{x^3}}}{9} - 3.\dfrac{{{x^2}}}{9}.6y + 3.\dfrac{x}{3}.36{y^2} - 216{y^3}\\ = \dfrac{{{x^3}}}{9} - 2{x^2}y + 36x{y^2} - 216{y^3} \end{array}$
