Does Ward trigger if the spell targeting the creature is cast with no mana cost like through cascade?

Ward is a triggered ability that triggers whenever the permanent with Ward becomes the target of a spell or ability an opponent controls (CR 702.143a). The trigger condition checks only whether the permanent was targeted, not how the spell was cast or paid for.

Cascade (CR 702.84) allows a player to cast a spell from exile without paying its mana cost. However, 'without paying its mana cost' is simply an alternative way to cast the spell — the spell is still cast, still goes on the stack, and still targets normally. Nothing about Cascade exempts the spell from causing Ward to trigger.

Once Ward triggers, the opponent must pay the Ward cost or the spell is countered (CR 702.143b). The Ward cost is completely separate from the original casting cost. So even though the opponent paid nothing to cast the Cascade-found spell, they must still pay the Ward cost if they want the spell to resolve and affect the protected creature.

Example: Your opponent controls a creature with Cascade and attacks. Cascade exiles a Lightning Bolt, which they cast for free targeting your creature with Ward {2}. Ward triggers. Your opponent must now pay {2} or Lightning Bolt is countered — despite having cast it for no mana originally.

This applies equally to other free-cast effects like Suspend, Evoke (paying the evoke cost), or cards that let you cast spells without paying their mana cost (e.g., Omniscience). Ward does not care about the payment method for the original spell.