In the complex $[Co(CN)_6]^{3-}$, the central metal ion is Cobalt (Co) in the +3 oxidation state. The electronic configuration of $Co^{3+}$ is $3d^6$. Since the cyanide ion ($CN^-$) acts as a strong field ligand, the crystal field splitting energy ($\Delta_o$) is greater than the pairing energy ($P$). This leads to the pairing of the six $d$-electrons in the lower energy $t_{2g}$ orbitals, resulting in a $t_{2g}^6 e_g^0$ configuration. Because all the electrons are paired up, the number of unpaired electrons is zero, making it diamagnetic. It forms an inner-orbital, low-spin complex.