The strong influence of nuclear spins on resonant quantum tunneling in the molecular cluster Fe8 is demonstrated for the first time by comparing the relaxation rate of the standard Fe8 sample with two isotopic modified samples: (i) 56Fe is replaced by 57Fe, and (ii) a fraction of 1H is replaced by 2H. By using a recently developed "hole digging" method, we measured an intrinsic broadening which is driven by the hyperfine fields. Our measurements are in good agreement with numerical hyperfine calculations. For T>1.5 K, the influence of nuclear spins on the relaxation rate is less important, suggesting that spin-phonon coupling dominates the relaxation rate.