Propagation and amplification of intense coherent laser pulses in a multicore fiber of 24 weakly coupled cores arranged in the form of seven close-packed hexagons were studied. Exact stable analytical solutions are found for the out-of-phase mode, which describes the coherent propagation of wave beams and temporal soliton solutions in such fibers. Their stability is demonstrated. The analytical results are confirmed by the direct numerical simulation of the wave equation.