Generally, how long does ice cubes last (until it melts) in a cooler box? Assuming the cooler is kept at room temp.

It will depend on
1. What that room temperature is
2. The size of the cubes, and
3. The type of cooler (http://www.igloocoolers.com/results?searchString=&activities[]=4741) you're using.

If this is an "actual use" type of question rather than a Chemistry one, I can say this:

When my family goes camping, we use a thick one with a good sealing lid - and ice blocks instead of cubes, and the ice lasts 3-4 days.

Hi,
As rickj stated, it depends on the type of cooler.
A Styrofoam cooler will usually keep ice cubes about 24 hours, maybe a little longer, depending on the outside temperature. Some of the larger, stronger coolers, won't keep them as long as a true Styrofoam cooler.