This is a black and white manga that I read in English recently, but on the internet. The original language might not have been English. Mechs aren't a thing, but armored vehicles do exist. I only got to around chapter 30, but below is my summary of the plot.
At the beginning of the story the main character is a black haired kid, and he meets another kid who becomes his best friend. This kid is beautiful (according to the dialogue), and has this shiny white hair. The best friend's sister is similarly beautiful, and the main character guy even runs away from her when they first meet.
They all grow up, but then one day the sister is sold off to the Emperor by her father, leaving behind a cake she baked. The main character and his best friend vow to get her back by taking control of the whole universe. They sign up to be officers in the Empire's military, go through school with top marks, then get assigned to a cushy position far behind the front lines. They request to instead go straight to the front lines, where a cabal of fellow soldier try to assassinate them on the orders of a duchess, who dislikes how the sister is taking up all of the Emperor's attention. The main duo power through, and are fairly successful.
They then go up into ships for space battles, where hundreds of thousands to millions of people die in each engagement. There is a giant laser called something like 'Thor's Eye' that is occasionally important. Occasionally, the duo return to the sister, and are sometimes given rewards by the Emperor for their results on the battlefield .