After the Muslim victory in the Battle of Badr, when the Muslims are on their way back to Medina, the following is reported in Ibn Hisham's "Sirat Rasul Allah" ...

When the apostle ordered him to be killed `Uqba said, "But who will look after my children?" "Hell", he said, and `Asim b. Thabit b. Abu'l-Aqlah al-Ansari killed him according to what Abu `Ubayda b. Muhammad b. `Ammar b. Yasir told me. [page 308] The apostle arrived in Medina a day before the prisoners. ... [page 309]

Mus`ab b. `Umayr ... said: "Bind him fast, for his mother is a wealthy woman; perhaps she will redeem him for you." ... [page 309]

Then the Quraysh sent to redeem their prisoners ... [page 312]

The Dictionary of Islam by T.P. Hughes gives the account in more detail based on other (sadly unnamed) sources, on page 376:
 

Two days afterwards [after Nadr bin al-Harith], about half-way to Medina, Ocba, another prisoner, was ordered out to for execution. He ventured to expostulate and demand why he should be treated more rigorously than the other captives. "Because of your enmity to God and to his prophet," replied Muhammad. "And my little girl! cried Ocba, in the bitterness of his soul, "who will take care of her"" "Hellfire!"

According to the Sirat, the prisoners captured at the battle are held for ransom and nearly all exchanged for money. Pages 309-314 in Ibn Hisham report about some of the transactions.

However, two people are singled out by Muhammad to be killed. Nadr bin al-Harith and `Uqba bin Abi Mu`ayt whose execution is the topic of the above paragraph.

We are not told very much about this person, other than that he went to Medina together with al-Nadr b. al-Harith to find some tough questions to pose to Muhammad in order to test him whether he was a genuine prophet. Certainly not something unreasonable. However, it seems that Muhammad considered him to be a personal enemy. Therefore he is executed on command of Muhammad. No proper trial or reason for the killing of the prisoner of war is given other than the statement "Because of your enmity against me". Is it allowed in Islam that the victor of a war kills some of the prisoners for reasons of personal enmity?

Is that how a true spokesman for the God of justice would act?

Even if the death penalty had been justified, was it necessary to add this mental torture to the execution of his enemy? What does Muhammad's response to the anguish of `Uqba over the future of his children reveal about his character?