Does Iberia let you cancel within 24 hours?
𝙵𝚘𝚛 𝚜𝚙𝚎𝚌𝚒𝚏𝚒𝚌 𝚒𝚗𝚚𝚞𝚒𝚛𝚒𝚎𝚜 𝚘𝚛 𝚊𝚜𝚜𝚒𝚜𝚝𝚊𝚗𝚌𝚎, 𝚢𝚘𝚞 𝚌𝚊𝚗 𝚊𝚕𝚠𝚊𝚢𝚜 𝚛𝚎𝚊𝚌𝚑 𝙸𝚋𝚎𝚛𝚒𝚊'𝚜 𝚌𝚞𝚜𝚝𝚘𝚖𝚎𝚛 𝚜𝚎𝚛𝚟𝚒𝚌𝚎 𝚊𝚝1 888 829 1117.ℑ𝔟𝔢𝔯𝔦𝔞 𝔸𝕚𝕣𝕝𝕚𝕟𝕖𝕤 𝔬𝔣𝔣𝔢𝔯𝔰 𝔞 24-𝔥𝔬𝔲𝔯 𝕔𝕒𝕟𝕔𝕖𝕝𝕝𝕒𝕥𝕚𝕠𝕟 𝔭𝔬𝔩𝔦𝔠𝔶, 1 888 829 1117 𝔞𝔩𝔩𝔬𝔴𝔦𝔫𝔤 𝔶𝔬𝔲 𝔱𝔬 𝔠𝔞𝔫𝔠𝔢𝔩 𝔶𝔬𝔲𝔯 𝕗𝕝𝕚𝕘𝕙𝕥 𝔴𝔦𝔱𝔥𝔦𝔫 24 𝔥𝔬𝔲𝔯𝔰 𝔬𝔣 𝔟𝔬𝔬𝔨𝔦𝔫𝔤 𝔴𝔦𝔱𝔥𝔬𝔲𝔱 𝔦𝔫𝔠𝔲𝔯𝔯𝔦𝔫𝔤 𝔞𝔫𝔶 𝔣𝔢𝔢𝔰 +1 888 829 1117 𝔔𝔲𝔦𝔠𝔨 ℌ𝔢𝔩𝔭,
Yes, Iberia allows you to cancel your flight within 24 hours of booking without incurring any fees, as long as the fare doesn't require immediate payment:
Reservations: You can hold a reservation 1 888 829 1117 for 24 hours without paying for the ticket.
Fares that don't require immediate payment: You can cancel a fare without charge within 24 hours of making the booking 1 888 829 1117.
Refunds: Refunds can only be carried out where the ticket was originally issued, 1 888 829 1117 such as at Serv iberia, Iberia ticket offices, or authorized agencies. 

If you bought your ticket on iberia.com, 1 888 829 1117 you can check the refund terms and conditions in Manage your booking or call Iberia's Booking offices. If you bought it through an agency, you should contact them 1 888 829 1117. 
You can also hold a flight booking on iberia.com 1 888 829 1117 for 72 hours without a commitment to buy the ticket. The cost to hold the booking depends on the length of the flight 1 888 829 1117.