Rutherford cables exhibit two classes of parasitic magnetization both of which can distort the bore-field of an accelerator magnet: (1) a static magnetization ("hysteretic") resulting from intrastrand persistent currents, and (2) a dynamic magnetization produced by interstrand coupling currents passing through interstrand contact resistances (ICR) during field ramping. Interstrand coupling can be controlled by a core placed between the layers of the cable. Stainless steel ribbon (with its associated native oxide coating) is a frequently used core. Recently, however, MgO-paper tapes and woven s-glass ribbons have been suggested as alternative core materials in the interests of improved flexibility and compatibility with the cabling process. Interstrand contact resistances can be extracted from the results of AC loss measurement. Accordingly pickup-coil magnetization measurements of AC loss have been carried out on a group of cables with paper and ribbon cores. This paper reports on the resulting ICR results which it compares to those from uncored and stainless-steel-cored cables; it concludes by comparing the LHC-ramp-rate induced coupling magnetization of a typical cored Nb 3 Sn Rutherford cable with its transport-current-moderated persistent-current magnetizations at low and high fields.