In your efforts to collect everything right you will find two Blackboxes during Crysis 3 Mission 1: Post-Human.
Blackbox location no. 1
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.