Welcome, here's the first step to contruct a 3D cube with perspective change: Fix your center and create three handles that will represent the three dimensions.
You can drag the handles around. Try it!
You can disable the debug (gray dotted lines) with the checkbox, and go to the next step with the step dropdown.
We compute the points at the center of the exiting lines.
We then create new lines between the handles and those new points, you can see the front of the cube starting to appear.
Now let's add the intersection points between all those new lines. They are the corners of our cube.
Maybe it's clearer with strong lines, can you see the cube now?
We have our three "front" faces of our cube, but the "back" ones are missing, let's add them now!
We can create the last point by finding the intersection between the lines from the handles to their oposite intersection points.
Let's remove all points and trace the remaining lines, and voilĂ !