Police detained eight players at the weekend in the city of Tampere where the Cuban men's team was playing in a World League tournament.
The suspected rape occurred at a hotel where the team was staying and was reported to police on Saturday. Two of the men were released on Monday and police said they were no longer suspects in the case.
The remanded players will remain in custody while the investigation continues, until prosecutors decide on possible charges.
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Finnish newspaper Helsingin Sanomat reported that all six men denied guilt in court.
Cuba is among the 12 teams qualified for the Rio Olympics men's volleyball tournament.
(Reporting by Tuomas Forsell; Editing by Janet Lawrence)
