There are a few possible candidates, but the most likely is the text known as the Counsels of Wisdom. This is a work found Late Babylonian copies but possibly of Kassite (post-Old Babylonian) date. The text can be found in W. G. Lambert, Babylonian Wisdom Literature (1960) pp. 96-106; also in Pritchard (ed.), Ancient Near Eastern Texts Relating to the Old Testament, 3rd ed. (1960) pp. 595-6.

Other possibilities are:

1. The Instructions of Shuruppak. This was actually my first thought, as it's probably the best example of the genre, but it's actually Sumerian in origin, though part of an Akkadian translation also survives (Pritchard p. 594-5). There's a 1974 edition by B. Alster; it's also in Lambert, pp. 92-5; here's an online copy, but the translation is uncredited, and therefore of doubtful accuracy. It's a bunch of advice from an ancient sage Shuruppak to his son Ziusudra (who ends up being the man who survives the flood) on things like buying livestock, crimes, and human nature.

2. A poem on agriculture, again Sumerian, that starts "In days of old a father instructed his son", with a heading describing it as the Instructions of Ninurta (a god).

3. An Akkadian work consisting of the instructions of Shube-amelim to his son Zurranku, found at Ugarit and in a Hittite translation at Hattusa.

There are also other examples of the same genre from other ancient Near Eastern cultures and from Greece, so you can see this was a fairly popular premise for a poem.