$B=\frac{{{\left( b-c \right)}^{3}}+{{\left( c-a \right)}^{3}}+{{\left( a-b \right)}^{3}}}{{{a}^{2}}\left( b-c \right)+{{b}^{2}}\left( c-a \right)+{{c}^{2}}\left( a-b \right)}$
$B=\frac{{{b}^{3}}-3{{b}^{2}}c+3b{{c}^{3}}-{{c}^{3}}+{{c}^{3}}-3{{c}^{2}}a+3c{{a}^{2}}-{{a}^{3}}+{{a}^{3}}-3{{a}^{2}}b+3a{{b}^{2}}-{{b}^{3}}}{{{a}^{2}}b-{{a}^{2}}c+{{b}^{2}}c-{{b}^{2}}a+{{c}^{2}}a-{{c}^{2}}b}$
$B=\frac{-3{{a}^{2}}b+3a{{b}^{2}}-3a{{c}^{2}}+3{{a}^{2}}c-3{{b}^{2}}c+3b{{c}^{2}}}{{{a}^{2}}b-a{{b}^{2}}+a{{c}^{2}}-{{a}^{2}}c+{{b}^{2}}c-b{{c}^{2}}}$
$B=\frac{-3\left( {{a}^{2}}b-a{{b}^{2}}+a{{c}^{2}}-{{a}^{2}}c+{{b}^{2}}c-b{{c}^{2}} \right)}{{{a}^{2}}b-a{{b}^{2}}+a{{c}^{2}}-{{a}^{2}}c+{{b}^{2}}c-b{{c}^{2}}}$
$B=-3.$