A binomial in the form $\displaystyle{{a}}^{{3}}-{{b}}^{{3}}\usepackage{cmbright}\Huge\$ can be factored as $\displaystyle{\left({a}-{b}\right)}{\left({{a}}^{{2}}+{a}{b}+{{b}}^{{2}}\right)}\usepackage{cmbright}\Huge\$ . Since $\displaystyle{27}{{x}}^{{3}}={{\left({3}{x}\right)}}^{{3}}\usepackage{cmbright}\Huge\$ , you should have replaced a by $\displaystyle{3}{x}\usepackage{cmbright}\Huge\$ . Whenever you factor, remember to check your answer by multiplying the factors back together. The correct answer is $\displaystyle{\left({3}{x}-{4}\right)}{\left({9}{{x}}^{{2}}+{12}{x}+{16}\right)}\usepackage{cmbright}\Huge\$ .