In the main room, there is a deadly laser up ahead, and an aerial faith plate that probably would catapult you directly into the laser's path if you stepped on it. So instead of doing that, make a portal way up on the wall opposite the cube that some platforms are bouncing around. Then go over to the deep pit on the side of the room and create a portal of the opposite color on the floor in there. Falling into that portal should fling you over to the cube. The platforms will stop playing with the cube after you land there. Use portals to take the cube to the main part of the room (you will have to jump down into the pit again, so just make a portal on some low wall in the main part of the room to come out of).
Put the cube onto the aerial faith plate. It looks like the cube didn't get zapped by the laser, so step on the aerial faith plate to land on the ledge with the cube. Put the cube in the path of the laser. You can set it down in front of the laser receiver. This will lower the glass wall in your way.
Drop back down to the main part of the room and step on the aerial faith plate again. This time, you will hit some aerial faith plates on the wall and get bounced up to a higher part of the room. There is a laser receiver here, and a portal wall across from it. Additionally, there is a small red button that will drop a laser redirection cube from the cube chute.
Before pressing the red button, shoot a portal into the wall facing the laser receiver. Then press the button. When the laser redirection cube lands nearby, pick it up and fall down to the level below. Put the laser redirection cube somewhere other than the glass panels in the floor, then remove the normal cube from the path of the laser. Put the laser redirection cube in the path of the laser such that it shoots at a portal wall, then shoot a portal of the other color on that wall (you can look up to see an outline of the other portal's color if you don't remember). This will lower the wall up above.
Pick up the normal cube and drop down to the lower level. While carrying it, step on the aerial faith plate. You and the cube will hit several aerial faith plates and eventually land on the ledge with the big red button that opens the exit door. Put the cube on the big red button and go down to the elevator.