Multistrand cables may 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 generated during field ramping. The latter, which are moderated by the interstrand contact resistances (ICR), can be controlled by the presence of an insulating core inserted 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 by LBNL (Lawrence Berkeley National Laboratory) as alternative core materials in the interests of improved flexibility and compatibility with the cabling process. This paper reports on the results of calorimetric AC loss (hence ICR) measurements on a set of four such cables and presents the results within the context of previously measured cored and uncored Nb3Sn cables. Also considered is a typical ramp-rate-induced coupling magnetization and its relationship to persistent-current magnetizations over the operating range of an accelerator magnet.