Cunill began his racing career in 2006, driving in the Copa de España class of the Spanish Formula 3 Championship. In the six races he competed in, he took three class podiums to finish 6th in the standings. He also participated in selected races of the Belgian Formula Renault 1.6 championship, scoring a single championship point.
For 2007, Cunill took part in a full Spanish F3 season, driving for GTA Motor Competicion. Over the course of the year, he took one podium place (in the final round at Barcelona) and three further points scoring positions to finish 14th in the championship.
In 2008, Cunill entered both the Eurocup Formula Renault 2.0 and Italian Formula Renault 2.0 championships, driving for Swiss team Jenzer Motorsport. In the six Eurocup races he contested his best result was a 6th place at Spa-Francorchamps, whilst in the Italian series he finished in the points in eight of his ten races, with his best result also being a 6th place finish.
In August 2008, he made his debut in the World Series by Renault with the KTR team after both of their regular drivers, Guillaume Moreau and Daniil Move, left the team. Despite only qualifying 23rd, he scored points in his debut race at the Nürburgring, finishing in 10th place after post-race penalties were handed to both Fairuz Fauzy and Esteban Guerrieri.
|2006||Spanish F3 Championship (Copa de España)||GTA Motor Competicion||6||0||0||?||3||23||6th|
|Belgian Formula Renault 1.6||?||5||0||0||?||0||1||21st|
|2007||Spanish F3 Championship||GTA Motor Competicion||16||0||0||0||1||19||14th|
|2008||Italian Formula Renault 2.0||Jenzer Motorsport||10||0||0||0||0||96||12th*|
|Eurocup Formula Renault 2.0||Jenzer Motorsport||6||0||0||0||0||5||20th*|
|World Series by Renault||KTR||6||0||0||0||0||1||30th*|
* Season in progress