An analysis is presented of inclusive π0 production in Z 0 decays measured with the DELPHI detector. At low energies, π0 decays are reconstructed by using pairs of converted photons and combinations of converted photons and photons reconstructed in the barrel electromagnetic calorimeter (HPC). At high energies (up to xp=2cdotp≪/sqrts=0.75) the excellent granularity of the HPC is exploited to search for two-photon substructures in single showers. The inclusive differential cross section is measured as a function of energy for qq̅ and bb̅ events. The number of π0"s per hadronic Z 0 event is N(≪0)/Z0had=9.2pm0.2(⤪stat)pm1.0(⤪syst) and for bb̅ events the number of π0"s is ⤪N(≪0)/⤪b⋏rb=10.1pm0.4(⤪stat)pm1.1(⤪syst). The ratio of the number of π0"s in bb̅ events to hadronic Z 0 events is less affected by the systematic errors and is found to be 1.09 ±0.05 ±0.01. The measured π0 cross sections are compared with the predictions of different parton shower models. For hadronic events, the peak position in the xi⤪p=⤪ln(1/⤪xp) distribution is xi⋆arp=3.90+0.24−0.14. The average number of π0"s from the decay of primary B hadrons is found to be N(B → π0 X)/B hadron = 2.78 ± 0.15(stat) ± 0.60(syst).