Triple King's Cup holders Barcelona were drawn against Celta Vigo in the last 16 on Tuesday, three days after being held to a 2-2 draw by the Galician team in La Liga.
Real Madrid were pitted against second division Numancia and Atletico Madrid face third tier Lleida Esportiu who came from behind to knock out Real Sociedad on away goals and reach the last 16 for the first time.
Formentera, the only other third-tier side left in the competition, will play last season's runners-up Alaves.
Second division side Cadiz will play Sevilla after dumping out Seville's other club Real Betis in the previous round with a 5-3 away win in the second leg.
The remaining ties are all top-flight affairs, with Valencia meeting Las Palmas, Leganes playing Villarreal and Levante facing Espanyol.
The ties will be played over two legs in early January.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)