Conductor on round core (CORC) cables wound by high-temperature superconducting (HTS) tapes have received much attention due to the advantages in power capacity and mechanical flexibility. This paper first developed a 3D model for a CORC cable through the finite-element method (FEM). Next, the total AC loss caused by transported current only was investigated, revealing the eddy current loss in the tube former contributes to the cable loss. The numerical CORC model was validated by published measurements. Moreover, the AC loss that resulted from a simultaneous presence of transport current and magnetic field was explored. With the induced current, the magnetisation loss generated in superconductors can increase the total loss. It is concluded that the addition of a magnetic field can result in a surge in the total loss of a current-carrying cable.