The invention relates to the making of boxes of a variable volume adapted in each case to the height of the packed products, including cutting the box along its vertical edges and forming fold lines at a suitable height around the sides of the box to define top flaps; and then folding these flaps onto the contents of the prefilled box. At least one inflated or inflatable void-filling bag is inserted into the box, around and/or above the packed products, after the fold lines have been formed, and before the flaps are folded onto the contents of the box. The invention also provides a combined machine that cuts, marks, prepares and inserts void-filling bags, and closes boxes.Applicable to order filling.