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