The electronic configuration of central metal atom/ion in ${\left[\mathrm{Co}(\mathrm{CN}{)}_6\right]}^{3-}$ is

oxidation state of Co in ${\left[\mathrm{Co}(\mathrm{CN}{)}_6\right]}^{3-}$ is +3 .

electronic configuration of Co⁺³ 3d⁶

${\mathrm{CN}}^{-}$ is strong field ligand all the electrons are paired in t_2g orbital. Thus electronic configuration is ${\mathrm{t}}_{2\mathrm{g}}^6{\mathrm{e}}_{\mathrm{g}}^0$