In your efforts to collect everything right you will find two Blackboxes during Crysis 3 Mission 1: Post-Human.
Blackbox location no.
Once the mission begins and you gain control over Prophet, leave the ship and proceed down the ramp. At the end of the ramp, to the left, there is a huge container and a fallen soldier. You will find the first blackbox next to the soldier.
Blackbox location no. 2
At the end of the mission, you will find a turret with two guards, and a locked door to the right. Hack the turret and open the door. When the door opens you will find a dead soldier and a blackbox next to him.