The wrench-closure workspace of parallel cable-driven mechanisms is the set of poses of their mobile platform for which the cables can balance any external wrench. The determination of this workspace is an important issue since the cables can only pull and not push on the mobile platform. This paper deals with the wrench-closure workspace of six-degrees-of-freedom (DOF) parallel mechanisms driven by m cables, m >= 7. The boundary of the constant-orientation cross sections of the wrench-closure workspace is shown to consist of parts of cubic surfaces and an efficient method that determine this workspace by delineating its boundary is proposed.