\[- \left( - 4x^{3}c \right)^{3} = - \left( ( - 4)^{3}\left( x^{3} \right)^{3}c^{3} \right) =\]
\[= - \left( - 64x^{9}c^{3} \right) = 64x^{9}c^{3}.\]