Does cascade allow you to cast the exiled card for free regardless of its mana cost?

Cascade is a triggered ability that triggers when you cast the spell with cascade. You exile cards from the top of your library one at a time until you exile a nonland card whose mana value is less than the mana value of the cascade spell. You may then cast that exiled card without paying its mana cost. All remaining exiled cards are put on the bottom of your library in a random order.

Casting a card without paying its mana cost (CR 702.85c) means you pay zero mana for it, regardless of what its normal mana cost would be. However, you must still follow all other normal casting rules — you must choose legal targets, you still choose modes on modal spells, and so on. If the card has an additional cost (like a kicker), you may choose to pay it, but you are not required to.

One important restriction: because you are casting it without paying its mana cost, if the exiled card has alternative costs involving colored mana (such as an X in its cost where X cannot be zero), X is set to 0 by default. The card is simply cast for free in terms of mana.

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 without paying its {R} cost — it costs you nothing — and it deals 3 damage to a target as normal.

The relevant rules are CR 702.85 (Cascade) and CR 601.2b (casting without paying mana cost). The card is exiled and cast as part of the resolution of the cascade ability, not as a separate action you take on your own.