Formed at Barcelona, where he made 30 total appearances, he also represented Deportivo and Granada in La Liga, additionally playing top-flight football in the Netherlands, Turkey, Israel and Japan.

[7] Cuenca made his official debut for Barça B on 4 September 2011, playing the last 29 minutes in a 4–0 away win against FC Cartagena and scoring the last goal of the match.

[8] On 19 October he made his first official appearance for the main squad, coming on as a substitute for David Villa in the dying minutes of the 2–0 home victory over FC Viktoria Plzeň in the group stage of the UEFA Champions League.

[9] On 25 October 2011, after another game on the bench, Cuenca made his La Liga debut, playing the full 90 minutes and being booked in a 1–0 away defeat of Granada CF.

[17] Cuenca made his debut for his new team 10 February 2013, against Roda JC Kerkrade at the Amsterdam Arena, assisting Daley Blind in his first ever goal for Ajax as the match ended in a 1–1 draw.

[23] Cuenca made his debut for the club on 23 August 2014, replacing Toché in a 2–1 away loss to Granada,[24] and scored his first goal eight days later, a last-minute equaliser in the 2–2 home draw against Rayo Vallecano.

[33] In January 2019, Cuenca went back abroad and signed a three-year contract with the option of a fourth at Sagan Tosu in Japan's J1 League.

[36] Cuenca had his first international call-up in November 2011, when Spain under-21 manager Luis Milla named him in a 20-man squad for European qualifiers against Estonia and Switzerland.