  The mass relation ${M_{0^{+}}+3M_{1^{+\prime}}+5M_{2^{+}}= 9M_{1^{+}}}$
miraculously holds for the $P$-wave charmonium $(c\bar{c})$ and bottomonium
$(b\bar{b})$ systems with soaring precision. The origin of such relation can be
addressed from Quark Models, and have been confirmed experimentally in a
limited number of cases. In this connection, we propose
$M_{0^{+}}+5M_{2^{+}}=3(M_{1^{+\prime}}+M_{1^{+}})$ as an extension to the
$P$-wave $B_{c}$ case. In order to test its applicability, we employ a variety
of Quark Model predictions for the $B_c$ mass spectrum. Our numerical analysis
confirms such formula is accurate up to very small deviations.
