In Pokemon Duel there are three different coloured cubes you can collect of differenet rarity that each have their own purpose. You will be given these cubes when you open Time Boosters and purchase Boosters from the Shop and by completing Quests. Occassionally you will get them as a Daily Mission reward. Basically, the more you play, the more cubes you will get. Listed below are the three types of cubes and what they are used for.
Green Cubes
These cubes are the minerals you can obtain that increase the Chain Level of a Pokemon. Whenever you level up the damage for a specific attack of your choice will increase. The cap is Chain Level 10, this means you have 10 points you can distribute between the attacks of each individual Pokemon.
Blue Cubes
These cubes are also known as Rare Metal and are used to increase your Pokemon's Exp. Level in the 'Fusion' menu. The amount of experience will vary from cube to cube, the maximum level is 5, and the experience needed to level up increases with each level gained.
Gold Cubes
These cubes are also known as Ingot and it can only be exchanged for Coins in the Shop (do not fuse Ingots with your Pokemon as you will only get one Exp. point per Ingot). To trade Ingots for Coins at the Shop select the 'Exchange Coins' icon on the bottom right and choose the Ingot you want to exchange. The rarer the Ingot is the more coins you will get for it. The Coins you receive can then be used to perform Fusion and to get a team evaluation in Quest mode.