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We present the first wide range (2 meV$-$5.5 eV) optical conductivity ofEuB$_6$ from reflectivity and ellipsometry measurements. Upon the ferromagnetictransition at T$_{c}$=15.5 K, interband transition $\sigma_{1}(\omega)$decreases at three different energy $\omega$=0.5, 1.4, 2.75 eV and the lostspectral weight is transferred to the Drude $\sigma_{1}(\omega)$ at$\omega<$0.33 eV. We succeeded in explaining this unprecedented multiple-energy$\sigma_{1}(\omega)$ change using LDA+U calculated band structure by Kunes andPickett (Phys. Rev. B, $\textbf{69}$,165111). Our finding supports stronglythat (1) EuB$_6$ is a semimetal and (2) the exchange-driven band splitting isthe primary source of the drastic $\rho(T)$ and $\omega_{p}^{2}$ changes at T$<$ T$_{c}$.Comment: 5 pages, 5 figure

Multiple-Structure Optical Spectral Weight Transfer in Ferromagnetic EuB6