An all-fiber 4-core Yb-doped laser with a cavity formed by fiber Bragg gratings directly inscribed in each core with femtosecond laser pulses and 4% Fresnel reflection from the output fiber end face is demonstrated. It has been shown that the diameter of the active fiber winding significantly affects the power distribution between the cores, since it affects both the pump power distribution and the cross-coupling between the cores. In particular, with an active fiber winding diameter of 21 cm, the cores behave independently, and the power is distributed almost evenly over all cores. With a winding diameter of 6.5 cm, the lasing is achieved almost exclusively from one core, and a mechanism of that radiation concentration based on bending induced stress in an active multicore fiber is proposed which explains the experimental data. By analyzing the optical and radio-frequency spectra of the output laser radiation, additional details of the 4-core fiber lasing are revealed. In particular, a narrowband (several longitudinal modes) lasing with periodic linear sweeping of central wavelength in time is observed and characterized in the multicore fiber laser, for the first time to our knowledge. It is shown that crosstalk of longitudinal modes arising from different cores is greatly enhanced in the case of a strongly bent fiber.