Is cycling a card from your hand considered a spell?
No, Cycling is an activated ability that you can only use while the card is in your hand. Casting a spell requires that you pay a cards mana cost printed in the upper right of the card.

702.27a Cycling is an activated ability that functions only while the card with cycling is in a player’s hand. “Cycling [cost]” means “[Cost], Discard this card: Draw a card.”
202.1 A card's mana cost is indicated by the mana symbols at the top of the card. ...
202.1a The mana cost of an object represents what a player must spend from his or her mana pool to cast a card. ...