Did Absalom have three sons, or no son to keep his name?

The first verse records sons born to Absalom; the second records what he said at a later time, when he had none. The most likely reason is that the three boys died young. Unusually for a Hebrew genealogy, they are not even named, while their sister is named and described, and Keil and Delitzsch and John Gill both take this to mean that the sons died young (in infancy, Keil and Delitzsch say), leaving only Tamar. A man whose sons had all died could truly say, “I have no son to keep my name in remembrance”, and in Israel the loss of a man’s name with his line was a grief the law itself tried to prevent (Deuteronomy 25:6).

The second verse does not say when the pillar was set up, only that Absalom “in his lifetime had taken and reared up for himself a pillar”. The writer mentions it after Absalom’s death, as a look back, to set the grand monument he had raised for himself beside the pit in the forest where he was actually buried under a heap of stones (2 Samuel 18:17). Nothing in either passage requires the sons to have been alive when he spoke.

Before the sons were born

Some suggest that Absalom set up the pillar before any of his sons were born, perhaps fearing he would have none. The text allows this, though Gill thought it less likely.

In case they were killed

Josephus says that Absalom meant the pillar to keep his name alive should his children be killed (Antiquities 7.10.3). On this reading he spoke while they lived, fearing for them. It is a later interpretation, and the Hebrew, ‘I have no son’, fits the first answer better.

The Bible does not record when or how Absalom’s sons died, so the answer rests on a reasonable inference from the two verses.