The Scottish Prison Service confirmed that Jack McKenzie died on Friday, September 3, but it has not yet revealed his cause of death.
The 20-year-old was remanded into custody earlier in 2021 after an appearance at Glasgow Sheriff Court.
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The Procurator Fiscal and Police Scotland have been informed of the situation.
In due course a Fatal Accident Inquiry will be held into the death of the 20-year-old inmate.