All involve decisions originally made by the platform to remove user content.
They include images of female breasts in a post about breast cancer, and an image of a dead child alongside text about whether retaliation was justified against China for its treatment of Uighur Muslims.
The board said Facebook users had submitted 20,000 suggested incidents for review since October 2020.
The arbitration body is inviting the public to comment on the cases - which have all been anonymised - over the next seven days.
If it opts to overrule or alter Facebook's original actions, the firm must both publicly respond and comply.
"Facebook has to follow our decision. And that means if they have taken content down, they have to put it back up. But they also have to use this as a guideline for other similar cases," said Helle Thorning-Schmidt, former Prime Minister of Denmark and an Oversight Board member.
She told the BBC the cases had come from around the world and were chosen to "raise questions" about Facebook's policies on hate speech, nudity, dangerous organisations and violence.
The board has not given a date to share its conclusions, but Facebook has previously said it expects cases to be resolved within 90 days, including any action it is told to take.
The six cases are:
- A screenshot of tweets by former Malaysian Prime Minister Mahathir Mohamad, in which he wrote that "Muslims have a right to be angry and kill millions of French people for the massacres of the past"
- Photos of a dead child, fully clothed, with text in Burmese asking why there was no retaliation against China for its treatment of Uighur Muslims
- Alleged historical photos of churches in Baku, Azerbaijan, with text saying that Baku had been built by Armenians and asking where the churches had gone
- Eight photographs on Instagram which included female breasts and nipples, with text in Portuguese about breast cancer symptoms
- An alleged quote by Nazi Germany's propaganda chief Joseph Goebbels
- A video about France's refusal to authorise hydroxychloroquine and azithromycin as treatments for Covid-19