Does cascade let you cast the exiled card for free or do you still pay its mana cost?

When a spell with cascade is cast, you exile cards from the top of your library until you exile a nonland card with a lesser mana value. You may then cast that card without paying its mana cost. This is explicit in the cascade rules (CR 702.85c).

Casting without paying the mana cost is a significant permission — normally you must pay a spell's mana cost unless an effect specifically says otherwise. Cascade is one such effect. You do not pay any generic or colored mana for the spell you find.

There are a few nuances to keep in mind: if the exiled card has an additional cost (like a kicker or an enlist cost), you may still choose to pay those optional costs on top of the free cast. Also, if the card has a mandatory additional cost, you must pay it. But the base mana cost itself is waived entirely.

Example: You cast Bloodbraid Elf (mana value 4). Cascade triggers and you exile cards until you hit Lightning Bolt (mana value 1, which is less than 4). You cast Lightning Bolt for free — you pay zero mana — dealing 3 damage to any target immediately.

All remaining exiled cards that were revealed but not cast go to the bottom of your library in a random order (CR 702.85c).