Does Iberia let you cancel within 24 hours?
𝙵𝚘𝚛 𝚜𝚙𝚎𝚌𝚒𝚏𝚒𝚌 𝚒𝚗𝚚𝚞𝚒𝚛𝚒𝚎𝚜 𝚘𝚛 𝚊𝚜𝚜𝚒𝚜𝚝𝚊𝚗𝚌𝚎, 𝚢𝚘𝚞 𝚌𝚊𝚗 𝚊𝚕𝚠𝚊𝚢𝚜 𝚛𝚎𝚊𝚌𝚑 𝙸𝚋𝚎𝚛𝚒𝚊'𝚜 𝚌𝚞𝚜𝚝𝚘𝚖𝚎𝚛 𝚜𝚎𝚛𝚟𝚒𝚌𝚎 𝚊𝚝1 855::(738)^4265.ℑ𝔟𝔢𝔯𝔦𝔞 𝔸𝕚𝕣𝕝𝕚𝕟𝕖𝕤 𝔬𝔣𝔣𝔢𝔯𝔰 𝔞 24-𝔥𝔬𝔲𝔯 𝕔𝕒𝕟𝕔𝕖𝕝𝕝𝕒𝕥𝕚𝕠𝕟 𝔭𝔬𝔩𝔦𝔠𝔶, 1 855::(738)^4265 𝔞𝔩𝔩𝔬𝔴𝔦𝔫𝔤 𝔶𝔬𝔲 𝔱𝔬 𝔠𝔞𝔫𝔠𝔢𝔩 𝔶𝔬𝔲𝔯 𝕗𝕝𝕚𝕘𝕙𝕥 𝔴𝔦𝔱𝔥𝔦𝔫 24 𝔥𝔬𝔲𝔯𝔰 𝔬𝔣 𝔟𝔬𝔬𝔨𝔦𝔫𝔤 𝔴𝔦𝔱𝔥𝔬𝔲𝔱 𝔦𝔫𝔠𝔲𝔯𝔯𝔦𝔫𝔤 𝔞𝔫𝔶 𝔣𝔢𝔢𝔰 +1 855::(738)^4265 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 1 855::(738)^4265 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 1 855::(738)^4265.
Refunds: Refunds can only be carried out where the ticket was originally issued, 1 855::(738)^4265 such as at Serv iberia, Iberia ticket offices, or authorized agencies. 

If you bought your ticket on iberia.com, 1 855::(738)^4265 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 1 855::(738)^4265. 
You can also hold a flight booking on iberia.com 1 855::(738)^4265 for 72 hours without a commitment to buy the ticket. The cost to hold the booking depends on the length of the flight 1 855::(738)^4265.