Born in Trujillo, Cueva started his career playing for amateurs Instituto Pedagógico Nacional Monterrico, at the age of 14.

[2] On 12 April 2008, aged only 16, Cueva made his first team – and Torneo Descentralizado – debut, coming on as a second-half substitute in a 3–1 away loss against Universidad César Vallejo.

[16] He made his debut for the club on 29 July, replacing Diego Aguilar in a 4–3 home defeat of Necaxa, for the year's Copa Mexico.

[19] However, he subsequently had multiple indiscipline problems, being fined twice and having a face off with teammate Rodrigo Caio due to the club's poor results.

[21] On 7 February 2019, Cueva returned to Brazil after agreeing to a one-year loan deal with Santos FC, with an obligation to buy on a three-year contract on 31 January 2020,[22] for an estimated fee of € 6 million.

[24] Santos president José Carlos Peres later requested the lining up of Cueva in a TV interview, which was later dismissed by the club's director of football Paulo Autuori.

[36] Cueva was included in Peru's squad for the 2015 Copa América,[37] and scored the team's opening goal of the tournament in a 2–1 loss to Brazil.

Cueva was also named in Ricardo Gareca's squad for the Copa América Centenario,[39] and scored the opening goal in an eventual 2–2 draw against Ecuador at University of Phoenix Stadium on 8 June 2016.

[48] His playing style has drawn comparisons with that of Brazilian playmaker Paulo Henrique Ganso, who plays for Sevilla, as Cueva occupies a similar function for São Paulo, in the way that he tends to move more through the pitch, making attacking runs into the rival area, scoring goals, and occasionally also helping out defensively by marking opponents.

[49] In his side's 4–0 victory against rivals Corinthians on 5 November 2016, Cueva demonstrated his great talent by netting a goal and providing three assists for his teammates David Neres, Chávez and Luiz Araújo.