I started my first mage build in Skyrim,

Like my ranger character, I only started investing build perks after Lv30. After reaching max enchant, contracting vampirism, adding Necromage perk, max alchemy and max most mage skills, I decided to create an enchanted set for the mage. The set reduced to 0 the cost ot illusion and destruction spells, conjuration and restoration spells are reduced 31%. My potions give 38% boost to enchanting. No surprise here. [Since I'm unable to post images, I couldn't host any screenshot]

After this, I thought I'd still be unable to cast the master spell Fire Storm for I don't have the required magicka and the master perk, but I was able to perform it with 0 magicka cost.

You can save up to 6 perks(if you invest them in smithing, you can create a powerful armor with a maxed out fortify smithing set) with an enchanted set and still be able to cast master spells with 0 magicka cost.

I've been playing Skyrim for over 300h and didn't knew about this trick.
Anybody knows if this is normal or a glitch?

It's a fresh and clean mod-free savegame, I only have Dawnguard installed.

its not a glitch or anything.

I would say just take the perks though, your are a better more well rounded character when you take the perks because it allows you to use fortify magicka or magicka regen enchantments or whatever other enchantment you would like. you would still use some reduce cost enchants, but rather than taking up 8 slots, it might only be 2-4.