Four were found guilty of beating Samiul Alam Rajon to death after they said he tried to steal a rickshaw. Six other men were jailed.
The murder, filmed by one attacker on his phone, caused widespread outrage.
In the second case, two car mechanics were condemned for the death of a former employee.
Rakib Hawlader died in August after air was pumped into his body in retaliation for leaving his job.
Rajon was attacked in July after a group of men accused him of stealing a bicycle rickshaw van in the north-western city of Sylhet.
One of the attackers filmed the assault on his mobile phone. The footage showed the boy being tied to a pole and hit repeatedly with a rod.
The video, which was posted on the internet, showed the boy pleading for his life and crying for water, and screaming: "Please don't beat me like this, I will die."
An autopsy found that the 13-year-old had 64 separate injuries.
Thirteen men were originally charged in the case, but three were acquitted. Six received sentences of between a year and life.
Kamrul Islam, described as the prime suspect, was one of those who received the death penalty.
He had fled to Saudi Arabia after the murder but was arrested less than a week later after officials were reportedly tipped off by members of the country's large expatriate Bangladeshi community. He was extradited in October.
One of the other four men condemned to death is on the run, and so was sentenced in absentia.