Blake and Tristan Barrass died after an incident at a property in Shiregreen on Friday, May 24.
The two boys were among six children taken to hospital after emergency services were called to the house, but Blake, 14 and Tristan, 13, were later pronounced dead.
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The four other children survived and have since been discharged from hospital.
Blake and Tristan’s mum, Sarah Barrass, 34, of Gregg House Road, Shiregreen and Brandon Machin, aged 37, of no fixed abode, have both been charged with murder and are remanded in custody with a provisional trial date set for November.
Barrass has also been charged with three counts of attempted murder against two other children.
A High Court injunction bans the identification of any of the four surviving children involved in the case.
South Yorkshire Police has warned that anyone who breaches the ban, which includes social media comments, could be charged with contempt of court.
The inquest into Blake and Tristan’s deaths is to be opened at the Medico Legal Centre in Sheffield at 10am.