Sevilla romped to a 6-1 win in their last-32, first leg at Sabadell at the end of October, when Aspas also netted a treble, and after winning the return 5-1 they will play Andalusian rivals Granada or Cordoba next month for a place in the quarter-finals.
Sabadell took a surprise lead in the 22nd minute at the Sanchez Pizjuan stadium in Seville when Juan Collantes converted a penalty before Kevin Gameiro struck for the home side 10 minutes before halftime.
Aspas, who is on loan from English Premier League club Liverpool, scored three goals in four minutes midway through the second half to underline Sevilla's dominance and substitute Gerard Deulofeu completed the rout in the 81st.
"Let's see if this can become a habit," Aspas, who has been unable to nail down a regular starting place in coach Unai Emery's side, told reporters.
"These three goals will do me good to keep on gaining in confidence," added the 27-year-old.
Real set up a likely last-16 clash against city rivals Atletico Madrid when they secured a 9-1 aggregate success against third-tier minnows Cornella on Tuesday.
Both ties were brought forward because of Real's participation in the Club World Cup this month as European champions and the resulting disruption to the La Liga calendar caused by the tournament in Morocco.
In last-32, first leg games, La Liga champions Atletico, who beat Real 2-1 after extra time in the 2013 Cup final at the Bernabeu, won 3-0 at third-tier Hospitalet.
The winner of a probable tie between Real and Atletico is likely to meet record winners Barcelona in the quarter-finals.
A second-string Barca, missing most of coach Luis Enrique's regular starting 11 including Lionel Messi and Neymar, thumped Huesca, another third-tier club, 4-0.
Ivan Rakitic opened the scoring in the 12th minute with a splendid free kick, Andres Iniesta struck on his return from injury four minutes later, Pedro made it 3-0 six minutes before halftime and a deflected effort from Rafinha completed the scoring in the 72nd.
Police were on high alert for Atletico's match, as well as for Deportivo La Coruna's first leg at home to Malaga, following the death of a Deportivo fan in fighting near Atletico's stadium on Sunday before the two teams met in La Liga.
Malaga took an early lead at Deportivo's Riazor stadium before the home side levelled midway through the second half and the match ended 1-1. The return legs are in two weeks.
(Writing by Iain Rogers, editing by Toby Davis)
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