Does cascade let you cast the revealed spell for free without paying its mana cost?

Cascade (CR 702.84) is a triggered ability that triggers when you cast the spell with cascade. You exile cards from the top of your library until you exile a nonland card with a lesser mana value than the cascade spell. You may then cast that exiled card without paying its mana cost.

Casting a spell 'without paying its mana cost' (CR 601.2b) means you don't pay the mana symbols in the upper-right corner. This effectively makes the spell free in terms of its normal cost. However, if the card has additional costs (like kicker or entwine), you may choose to pay those on top. If it has mandatory additional costs, you must pay them even though you skip the mana cost.

One important restriction: you cannot choose to cast an alternative cost (such as a different permissive alternative cost) instead when casting via cascade — you are already using 'without paying its mana cost' as the permission and cost modification (CR 702.84c).

Concrete example: You cast Bloodbraid Elf (mana value 4) and cascade triggers. You flip cards until you hit Lightning Bolt (mana value 1, which is less than 4). You cast Lightning Bolt without paying its {R} cost — it deals 3 damage for free.

All remaining exiled cards that were not cast are put on the bottom of your library in a random order (CR 702.84b).