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\$ .

$\displaystyle{{x}}^{{3}}-{1},{000}={{x}}^{{3}}-{{10}}^{{3}}\usepackage{cmbright}\Huge\$ , so $\displaystyle{a}={x}\usepackage{cmbright}\Huge\$ and $\displaystyle{b}={10}\usepackage{cmbright}\Huge\$ .

This can be factored as

$\displaystyle{\left({x}-{10}\right)}{\left({{x}}^{{2}}+{10}{x}+{{10}}^{{2}}\right)}={\left({x}-{10}\right)}{\left({{x}}^{{2}}+{10}{x}+{100}\right)}\usepackage{cmbright}\Huge\$ .