The Commonwealth Games are held every four years (in between Olympic Games years), with participant nations and territories from the Commonwealth members participating (71 teams from 53 members). Most were formerly part of the British Empire or constitutionally linked with members who were, with Mozambique being the only exception. The Commonwealth Games evolved from the British Empire Games which began in 1930.
Just recently this year (27 September to 6 October), the French Jeux de la Francophonie was held. Participants were members of Organisation internationale de la Francophonie (56 member nations, 3 associate members and 14 observers). Many were former French colonies, but most united by the French language. Mozambique is an observer. The games were first hosted in 1989 in Rabat and Casablanca in Morocco.
Only a few months earlier this year, the Portuguese Jogos da Lusofonia was held. Participants were members of Comunidade dos Países de Língua Portuguesa (11 members). Most were former Portuguese colonies and united by the Portuguese language. Mozambique is definitely a member. The games were first hosted in 2006 in Macau, China.
Unusually, Spain, former members of the Spanish Empire and Spanish-speaking nations have not yet united to hold their own games in this manner. Should they do one day, Mozambique would probably also want to participate.