The cases were dealt with separately by Judge Leo Malone at Cork District Court yesterday.
All three arrests were made by gardaí from the Douglas area of the city.
The alleged offences relate to various dates in 2009 and 2010.
Judge Malone adjourned all three cases until dates next month to allow time for further direction from the Director of Public Prosecutions.
Each case will go from Cork District Court by indictment to Cork Circuit Criminal Court.
Garda Seán Minihan arrested Conor Murphy, aged 46, of Diamond Hill, Monkstown, Co Cork, and charged him with knowingly having 589 child pornography image files between Mar 31, 2010, and July 9, 2010.
Insp Bill Duane said the DPP had directed trial by indictment in that case. He said he believed the book of evidence was ready and he had no objection to the accused being remanded on bail until Dec 21.
Defence solicitor Emmet Boyle had no objection to that application in Mr Murphy’s case.
Garda Minihan also arrested a second man in an unrelated case yesterday.
Patrick Bracken, aged 49, of 48 Ardfallen Estate, Douglas Rd, Cork, was charged with possession of 158 child pornography images and 26 child pornography videos at his home on Jun 23, 2009.
The case was adjourned to Dec 14, and there was no objection to bail. Mr Boyle represented Mr Bracken, who is unemployed, on free legal aid.
Det Garda Aonghus Cotter arrested Patrick Enright, aged 23, of 7 Wainsfort, Rochestown Rd, Douglas, yesterday and charged him with possessing 500 images and 15 videos of child pornography on Aug 21, 2009.
Mr Enright, who is unemployed, was represented on free legal aid by Mr Boyle and the case was adjourned to Dec 14.
In the cases of Mr Bracken and Mr Enright, the DPP consented to summary jurisdiction on a plea of guilty but Judge Malone refused to accept jurisdiction.
The three cases are not linked.