Laternenschein

A cleave cost is an alternative cost that's paid instead of the spell's mana cost. Casting a spell for its cleave cost doesn't change the spell's mana value.

If an effect allows you to “cast a spell without paying its mana cost,” you can't cast that spell for its cleave cost.

If you cast a spell for its cleave cost, that spell doesn't have any of the text in square brackets while it's on the stack.

If you're paying the cleave cost, you choose the value of X.

You can't cast a spell for both its cleave cost and another alternative cost. For example, if an effect gives an Alchemist's Retrieval in your graveyard a flashback cost of {U}, you can't cast it from your graveyard for its cleave cost.