Cure Light Wounds targets a creature touched and Constructs are creatures. Therefore, you can cast a Cure Light Wounds spell on one. They are not living creatures, so they are not healed by the spell, nor are they undead, so they won't take damage. They (generally) don't have any other abilities that specifically interact with positive or negative energy or with Cure spells.
The Cure Light Wounds spell won't have any effect in and of itself on a Construct, although you might be able to add one with metamagic or other abilities that add rider effects to a spell.