Find the value of : \( x^3 + y^3 – 12xy + 64 \) when \( x + y = -4 \)

\[ x^3 + y^3 – 12xy + 64 \] \[ = x^3 + y^3 + (-4)^3 – 3xy(-4) \] \[ = x^3 + y^3 + (-4)^3 – 3xy(x+y) \] \[ \text{Since } x+y+(-4)=0 \] \[ \therefore x^3+y^3+(-4)^3=3xy(-4) \] \[ \therefore x^3 + y^3 – 12xy + 64 = 0 \]