Does the sole surviving brother inherit his two deceased, childless brothers, or do the four nephews of the previously deceased brothers have a share in their uncles' inheritance?

The inheritance of the deceased goes to his full brother or his father, and nothing to his nephews, because the brother excludes the nephew with an exclusion of deprivation.

Thus, the aforementioned man inherits the estate of his two brothers, not their other nephews, if they left no other heir.

It must be noted that matters of inheritance are very serious and cannot be resolved by a mere fatwa. Rather, they must be referred to the Sharia courts for investigation, as there might be another heir, wills, debts, or rights that take precedence over the rights of the heirs.