The trust, which runs the Queen's Medical Centre and City Hospital, pleaded guilty to failures to provide safe care and treatment to the three babies and their mothers, resulting in harm or loss, at Nottingham Magistrates' Court.
Kahlani Rawson, who died at four days old at City Hospital on June 15, was similarly failed by staff, the court heard, who misinterpreted CTG scans, causing a delay in his delivery.
Adele O'Sullivan, Kahlani Rawson and Quinn Parker died within four months of each other in 2021 while under the care of Nottingham University Hospitals (NUH).
The court heard the parents of Quinn - Emmie Studencki and Ryan Parker - were not properly consulted or told to look out for danger signs in the days leading to his death at just one day old.
Ahead of the hearing, NUH chief executive Anthony May said: “The mothers and families in these cases have had to endure things no family should after the care provided by our hospitals failed them, and for that I am truly sorry.