Mezue ahịrịokwu na-esonụ: Cuadrado mere egwuregwu mba ụwa mbụ ya n'afọ 2010, ma nweela 100 caps. Ọ bụ akụkụ nke ndị otu Colombia nke sonyere na mbipụta ise nke Copa América (2011, 2015,
2016, 2019 na 2021), na-eru quarter-finals ugboro atọ, ma na-enye aka na njedebe nke atọ ha na 2016 na 2021; Cuadrado nọchitekwara anya mba ya na mbipụta abụọ nke FIFA World Cup, na 2014 na 2018.