Bound states in the continuum (BICs) have unique properties and significant applications in photonics. In this paper, we show analytically and experimentally the existence of (N−1) BICs (multi-BICs) in the flat band of a periodic photonic comb made of N stubs of length d2 separated by segments of length d1. These BICs occur when d1 and d2 are taken commensurate at a given frequency, which turn to quasi-BICs (multi-Fano resonances) when d1and d2 are taken slightly different from the BIC position. The signature of BICs and quasi-BICs can be observed in the transmission and density of states (DOS) spectra. We show that BICs are characterized by an infinite Q factor resonances, while quasi-BICs give rise to high-Q factor resonances that grow cubically with N. Our study improves the theoretical comprehension of BICs in stubbed structure and provides useful guidelines for future applications.