The structural, electronic, and elastic properties of pristine and carbon-doped boron suboxide (B6O) are calculated using density functional theory. The results indicate that it is energetically preferable for a single carbon atom to substitute into an oxygen site rather than a boron site. The lattice parameters and cell volume increase to relieve the residual stress created by the carbon substitution. The interstitial position is not favorable for a single atom substitution. However, if two carbon atoms substitute for two neighboring oxygen atoms, then it becomes energetically favorable to dope an interstitial oxygen, boron, or carbon atom along the C-C chain. If the interstitial dopant is either boron or carbon, a local B4C-like structure with either a C-B-C or C-C-C chain is created within the boron suboxide unit cell. The resulting structure shows improvements in the bulk modulus at the expense of the shear and Young's moduli. The moduli further improve if an additional carbon is substituted within a polar or equatorial site of the neighboring B-12 icosahedron. Based on these calculations, we conclude that carbon doping can either harden or soften B6O depending on the manner in which the substitutions are populated. Furthermore, as B6O samples are often oxygen deficient, C doping can occupy such sites and improve the elastic properties.