The path to the cube is blocked off after Leap Of Faith, Logic 101 or A Jump Too Far has been solved. These puzzles trigger a transformation of the There's No Way In room and it becomes impossible to access the pink cube secret room. It must be accessed at the very beginning of the game.
At one end of There's No Way In in its initial version, there is a set of green-colored stairs with a yellow and black border. Walking down these stairs and then back up them will bring you to a room with two pyramids, one cyan and one magenta.
The pink cube is behind the cyan pyramid. Looking at the cyan pyramid triggers the pink cube and it will be audibly moving toward The Character. The pink cube will will reveal itself and will follow a path down the cyan pyramid, audibly under the floor, up the magenta pyramid, and audibly down the other side. The character must be looking at where the pink cube is audibly for the cube to complete the journey.
The first pink cube can be found in the gallery located at Three Paths In Sight, its path borders the room starting at the left and going around clockwise till it, on the right, disappears.
The second pink cube is bugged and unobtainable. There is, however, a clipping glitch that can be used to obtain it. This pink cube can be found by walking to the very back of the gallery and walking through the open window; while in the room with Noclip, you can run through the right wall and find the cube.
One can be found at the Window Of Opportunity. Transport to blue then walk around the transporter window so the red can be seen but don't trigger the transporter, now the other side is green. Transport to green and repeat the walk around, now the green side is pink. The pink cube follows the path in the shape of the number two.
The pink cube is Down The Rabbit Hole at the bottom. Chained jumps is the only way to reach the bottom since there is a Disintegrator Field in the shaft. Timing jumps precisely when The Character hits the Jump-pad pushes the jump-pad down. The initial fall to the jump-pad gives momentum to quickly traverse down.
The pink cube is inside the fake wall which also has a fake ceiling, use cubes to pillar upward and at the top is the pink cube.
The pink cube is behind the door to the left. Use cubes to either build a staircase or pillar upward to get up the fake stairs where the pink cube is.
After getting up the wall, crossing the appearing platform, and getting to the bottom of the Jump-pad, there is a wall at the back of the jump-pad shaft that is made of green cubes. The pink cube is behind the wall.
Between the window to the Yellow Gun platform and the sign there is a fake wall on the right where the pink cube is.
The pink cube is in the room just above above the ground-level entrance. Use the Yellow Gun to move the yellow cube close and use the cube for a lift.
A stairway materializes as you walk forward. Jump to fall through and walk forward through the wall to find the pink cube.
Stand on the pink ring, while looking at it, use blocks to pillar upward to the pink cube.
The pink cube is unobtainable without Noclip. It is located underneath the black circle on the ground between "WTF?" and "HMM..."
Enter the chase. When you see The Black Ghost float upwards, turn back and down the green staircase. There is now a door there. Behind it is the pink cube.