Drawing a cube and making in golden ration makes no sense to me because by definition they are two different things. The golden ration is not a rule nor design requirement. That ratio that has been establish over the years to make the aesthetics of items look pleasing so it is not absolute. It is common practice to design say chest of drawers with the drawers meeting it as the size changes from large height to much smaller at top while keeping the ration w x L of any drawer meeting the ratio. That is done by using a recursion formula. You could make the side look that way by some small added detail. You could make the project area of the slant x L of top may accomplishing what you want.
My question : Why do you have to be so precise??