We propose an innovative fast 3D approach for the accurate computation of electromagnetic losses in the metallic armors of submarine cables. In order to develop a scheme that is more efficient with respect to most commonly used 3D simulation methods, typically based on the Finite Element Method (FEM), we proceed by proposing a suitable discretization of an integral formulation. In the proposed approach, each wire of the armor is modeled as filamentary which leads to a dramatic reduction in the number of degrees of freedom in the numerical model and in the overall computational burden. The new approach can be applied to cables where armor wires are stranded either with opposite (contralay) or same (equilay) orientation as the central phase cables. The efficiency of the proposed method is especially notable in latter case for which FEM is very demanding due to the extremely large model size. The reduction in both computation times and memory footprint allows performing extensive sensitivity studies with respect to geometrical parameters and material properties that would be otherwise unaffordable with existing 3D methods.