The electronic configuration of central metal atom/ion in [Co(CN)₆]^3– is

 Co⁺³ ion is present in [Co(CN)₆​]⁻³.
While in the excited state, and undergoing hybridization, CN⁻ being a strong field ligand forces the inner d electrons to pair up.
 Co⁺³ in [Co(CN)₆​]⁻³ has no unpaired electron(i.e. it is diamagnetic).

d6 configuration with strong field ligand ${{\mathrm{t}}_{2\mathrm{g}}}^6{{\mathrm{e}}_{\mathrm{g}}}^0$