The adsorption properties and most possible interactions of hydroxyurea (HU), 5-fluorouracil (5-FU), carmustine (CMU), 6-mercaptopurine (6-MP), ifosfamide (IFO), and chloromethane (CM) anticancer drug molecules with g-BC6N nanosheet were explored using density functional theory (DFT) in both gas and water solution at B3PW91/6-31G(d,p) level of theory. The various orientations for the interaction of drug molecules with the g-BC6N nanosheet revealed that adsorption energy values were strengthened and favored when drug molecules interact with the boron atom (B73) on the edge side of the g-BC6N nanosheet through their oxygen or nitrogen atoms. The most stable structure was observed for the 6-MP/g-BC6N complex with the adsorption energies of −18.19 and −23.53 kcal mol−1 for configurations M1 and M2 in the gas phase, respectively. The values of adsorption energies showed a slight increase in the stability of drug/g-BC6N complexes by the inclusion of water solution as a preferred environment for drug delivery systems. Quantum theory of atoms in molecules (QTAIM) analysis revealed the presence of electrostatic with partially covalent interactions in all complexes. Frontier molecular orbital analysis (FMO) showed that the energy band gap (Eg) of g-BC6N nanosheet is significantly reduced after drug adsorption. Furthermore, UV–Vis absorption spectrum analysis revealed a redshift for HU/g-BC6N, 5-FU/g-BC6N, CMU/g-BC6N, and 6-MP/g-BC6N complexes, while a blueshift was observed for CM/g-BC6N complex. Finally, physisorption of drug molecule by g-BC6N nanosheet leads to a lower recovery time and higher facility of drug release for all systems, which is suitable for drug delivery applications.