Bring the sugar and rum to a boil in a medium saucepan. Cook for 3 minutes, until candy thermometer reads 234 degrees F.
Remove from heat and add the cashews, stirring constantly to coat with syrup. The sugar will become white and grainy after about 30 seconds.
Return saucepan to heat and re-melt sugar, adding a few drops of water if needed. Watch carefully, do not burn. When the syrup has turned a rich caramel color, about 2 minutes, and the nuts sound hollow at the tap of a spoon, remove from heat and stir in butter.
Transfer mixture to oiled baking sheet, spreading out in one layer, separating any pieces that are stuck together.