We construct the concept of complex cubic neutrosophic subbisemiring (ComCNSBS). We analyze the important properties and homomorphic aspects of ComCNSBS. For bisemirings, we propose the ComCNSBS level sets. A complex neutrosophic subset Γ if and only if each non-empty level set R(℘,κ), where ... is a ComCNSBS. We show that homomorphic images of all ComCNSBSs are ComCNSBSs, and homomorphic pre-images of all ComCNSBSs are ComCNSBSs. We illustrate the practical significance of our findings.