We studied local magnetic properties of triple-CuO2-layer superconductors HgBa2Ca2Cu3O 8+δ with rich 63 Cu isotope (underdoped Tc = 124 K and optimally doped Tc = 134 K) by 63 Cu NMR spin-echo techniques. The temperature dependences of the 63 Cu nuclear spin-lattice relaxation rate 63 (1/T1) and the spin Knight shift 63 Kspin of the inner plane Cu(1) site were nearly the same as those of the outer plane Cu(2) site in the normal states. The pseudogap temperature T * defined as the maximum temperature of 63 (1/T1T ) was 190 K for the underdoped Tc = 124 sample and 143 K for the optimally doped Tc = 134 K sample. The NMR results indicate the uniform hole distribution in the three layers, which is consistent with a coalescence of three-derived Fermi surfaces predicted by a band theory. The room temperature in-plane 63 K ab spin depends on whether the number of CuO2 planes per unit cell is even or odd for the Hg-based multilayer cuprate superconductors.