We have studied the mass spectra of doubly charmed pentaquark states in the Λc(*)D(*) and Σc(*)D(*) channels with JP=1/2±, 3/2±, and 5/2± within the framework of quantum chromodynamics sum rules. We use the parity projected sum rules to separate the contributions of negative and positive parities from the two-point correlations induced by the pentaquark interpolating currents. Our results show that the bound states of Pcc pentaquarks may exist in the ΛcD(12−), ΣcD(12−), ΣcD*(32−), Λc*D(32−), Λc*D*(52−) channels with negative-parity and ΣcD(12+), ΣcD*(32+), Σc*D(32+) channels with positive-parity, since their masses are predicted to be lower than the corresponding meson-baryon thresholds. However, they are still allowed to decay into the Ξcc(*)π final states via strong interaction. The triply charged Pcc+++(ccuud¯) and neutral Pcc0(ccddu¯) in the isospin quartet would definitely be pentaquark states due to their exotic charges. We suggest searching for these characteristic doubly charmed pentaquark signals in the Pcc+++→Ξcc(*)++π+/ρ+, Σc(*)++D(*)+ and Pcc0→Ξcc(*)+π−/ρ−, Σc(*)0D(*)0 decays in the near future. Published by the American Physical Society 2024