[6] He scored his maiden goal for his new side in the first leg of 2014–15 Albanian Cup second round versus Lushnja, netting in a 79th minute via a free kick.
[11] On 18 June 2018, Cuculi announced his departure from club along with team captain Ferhan Hasani, with the players refusing to sign contract extensions.
[12] On 13 August 2018, Kukësi announced to have signed Cuculi on a one-year contract, marking the return of the defender in the Albanian Superliga after three years.
[14] Cuculi made his official debut in the opening week of 2018–19 Albanian Superliga against Laçi, playing full-90 minutes as the match ended in a 1–1 draw.
[16] Cuculi earned his first cap for Macedonia on 26 May 2014 in a friendly match against Cameroon, entering in the field in 26th minute by replacing the injured Goran Popov as the team lost 2–0.