I was studying the nature of singularities of cubic hypersurface on $\Bbb P^{n+1}$. The chosen form was $$f(x_0,x_1 \dots , x_{n+1})=x_0^3+x_1^3+\dotsb+x_{n+1}^3-c(x_0+x_1+\dotsb+x_{n+1} )^3=0.$$ I wonder if this equation introduces a special cubic hypersurface. Please if you know the name of it inform me.