I am a pure mage and was wondering if there is any advantage in using no armor VS light armor?

No. Only if you want mage armor perks, then you need to wear clothe only. You can enchant clothe or armor with the same enchantments though.

There are a couple advantages to avoiding armor and using robes/clothes aside from enjoying the benefits from the mage armor perks.

For one thing, you can sneak much more quietly and get a good look around before you start fighting. For another, you are way lighter so you can carry more loot!

Mage armor perk (CRUCIAL if you are a mage who uses flesh spells), and for RP purposes require no armor rating (I dont think the lord stone armor rating counts against the perk and definitly no the rp though fyi)

A significant bonus to no armor for a mage is that the robes provide far better magicka recover and cost reduction compared to armor unless you get a very good enchanted briastplate. Even then that briastplate will only work for one school of magic for Fortify Magic Skill, unless you are master enchanter, whereas the underrated magicka regen effect helps all of your schools.

You can walk around town dressed more like a normal person as opposed to, you know, leather straps and buckles and such. Unless of course you're into that sort of thing...

now i cant get the image of a dragonborn with a gimp mask getting crushed by a dragon out of my head.