Femtosecond inscription of fiber Bragg gratings (FBGs) in each core of a cladding-pumped seven-core Yb-doped fiber enables efficient (≈70%) 1064-nm lasing in a robust all-fiber scheme with ≈33 W power, nearly the same for uncoupled and coupled cores. However, the output spectrum is quite different: without coupling, seven individual lines corresponding to the in-core FBG reflection spectra sum up into a broad (0.22 nm) total spectrum, whereas the multiline spectrum collapses into a single narrow line at strong coupling. The developed model shows that the coupled-core laser generates coherent superposition of supermodes at the wavelength corresponding to the geometric mean of the individual FBG spectra, whereas the generated laser line broadens, with a power (0.04-0.12 nm) like the single-core mode of a seven-times larger effective area.