Motivated by the recent experiment of the non-BCS scaling relation of the condensation energy $Delta CE$ vs. $T_c$ ($Delta CE sim T_c ^{beta}, betaapprox 3.5$) [PRB 89 140503 (2014)] for the Fe-based superconductors, we studied the CE and $T_c$ of the multiband BCS superconductors. We showed that the experimentally observed anomalous scaling relation $Delta CE sim T_c ^{3.5}$ is well reproduced by the two-band BCS superconductor paired by a dominant interband interaction ($V_{inter} > V_{intra}$). Our result implies that this seemingly non-BCS-like scaling behavior, on the contrary to the common expectation, is in fact a strong experimental evidence that the pairing mechanism of the Fe-based superconductors is genuinely a BCS mechanism, meaning that the Cooper pairs are formed by the itinerant carriers glued by a pairing interaction.
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