The mass and leptonic decay constants of recently observed two new excited $B_c$ states at LHC are studied within the QCD sum rules. Considering the contributions of the ground and radially excited states, the mass and residues of the excited states of pseudoscalar and vector mesons are calculated in the framework of two different approaches of the QCD sum rules, namely, linear combinations of the corresponding sum rules and its derivatives as well as QCD sum rules with the incorporation of the least square fitting method. The obtained results on mass $m_{B_c^+}(2S) = 6.88 \pm 0.03~\rm{GeV} $ and $m_{B_c^{*+}}(2S) = 6.94 \pm 0.03~\rm{GeV} $ are in good agreement with the experimental data. Our predictions for the decay constants of these states are: $f_{B_c^+}(2S) = 0.42 \pm 0.02~\rm{GeV} $ and $f_{B_c^{*+}}(2S) = 0.46 \pm 0.01~\rm{GeV}$, which can be checked at future experiments to be conducted at the LHC. Comparison of our results with the predictions of the other approaches on mass and residues is also presented.

11 pages, 4 figures Misprints are corrected and reference list has been updated