Bloodbraid Elf

If a spell with cascade is countered, the cascade ability will still resolve normally.

If you cast a card "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, you must pay those to cast the card.

Cascade triggers when you cast the spell, meaning that it resolves before that spell. If you end up casting the exiled card, it will go on the stack above the spell with cascade.

A spell's mana value is determined only by its mana cost. Ignore any alternative costs, additional costs, cost increases, or cost reductions.

When the cascade ability resolves, you must exile cards. The only optional part of the ability is whether or not you cast the last card exiled.