This question is about the warforged race presented in Unearthed Arcana: Eberron.
Based on this Tweet, by Mike Mearls I understand that a Warforged unit is a 'Living Construct':
cure wounds works on [warforged], stuff that works on living or construct works on them
This goes to say it has both the 'Living' and 'Construct' creature tag (if living was a tag). This means cure wounds does not work on constructs by themselves, but it does work on living creatures. Since Warforged also count as living, this makes them legal targets for cure wounds.
If it is affected by things that affect both living creatures and/or construct creatures; they have both the strength and weaknesses of both. What are the full implications of this?