During his professional career that spanned more than twenty years, Cubero played predominantly for Vélez Sarsfield, winning five league titles with the team (spread over three different decades) and becoming the most capped player in the club's history (counting both domestic and international competitions).

He was however a regular starter (mainly as right back, but sometimes also as defensive midfielder) in his team's 2005 Clausura winning campaign, where he also scored the first goal against Estudiantes de La Plata in a 3–0 victory that confirmed Vélez as champions.

However, when Ricardo Gareca took the manager position in Vélez for the Clausura tournament (second half of the season), Cubero started playing as right back.

On August 15, 2010, Cubero reached 300 professional games with Vélez (counting league and international competitions) during the 2010 Apertura second fixture win against All Boys.

[3] During the 2012 Inicial, Cubero played his 457th official game with Vélez, equating Pedro Larraquy as the most capped player in the club's history,[4] a record that he later surpassed.