I'm not sure how to create a certain block effect

So I’ve played the game Boundless, and I’m interested in how they made the blocks not quite straight looking and how they change when connected to other blocks.

I’m not sure what terms would make this question easier to express, and I’m not sure if it’s specifically a blueprinting subject, but I would like to gain some footing before I head into my next group project at school.

My idea was to make a something similar in gameplay to TLoZ:LttP, except with an art style similar to 3D Dot Game Heroes and Boundless. I feel that having naturally varied blocks would add a good feel to the overall presentation.