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We report electronic Raman scattering measurements on Ba(Fe1?xCox)2As2 (x=0.065 and 0.2) single crystals with Raman shifts from 9 cm?1 up to 600 cm?1 in the symmetry of B1g with respect to 1 Fe unit cell. When the crystals are cooled down, the evident quasielastic peaks of Raman spectra occur only in the crystal with x=0.065, which is due to the contribution of orbital ordering between xz and yz Fe 3d orbitals as we reported in another work. Here, we analyze the Eg phonon at 128 cm?1 which has the same function form of its Raman tensors as those of xz and yz Fe 3d orbitals in these two crystals respectively. Unlike their electronic continuums, no anomalies are found in the Eg phonons of these two samples, which simply follows the expressions corresponding to the anharmonic phonon decay into acoustic phonons with the same frequencies and opposite momenta. Our results indicate that the structural and magnetic phase transition might be completely suppressed by chemical doping and there is not any indication of coupling between charge nematicity and Eg phonon mode from our experimental results, which is consistent with the results in our previous work.