Ответ:

[tex] \displaystyle \frac{ {a}^{6} }{27} - 8 {b}^{3} = \frac{ { ({a}^{2} )}^{3} }{ {3}^{3} } - {2}^{3}{b}^{3} = ( \frac{ {a}^{2} }{3} - 2b)( \frac{ {a}^{4} }{9} + \frac{2 {a}^{2}b }{3} + 4 {b}^{2} )[/tex]