A decorative solid is made from a frustum of a right circular cone, with a $6$-inch height, an $8$-inch-diameter base at the bottom, and a $4$-inch-diameter base at the top. A solid cone is placed on top of this frustum, whose base, at the bottom, is the top base of the frustum, and whose height is $3$ inches. What is the total volume of the decorative solid, in cubic inches?