So you want to build your own colorful LED video cube? Adafruit has you covered. The Adafruit Video Cube has 1024 LEDs on each side (total of 6144 LEDs). You need video decoder boards, a HDMI connection, a 5V power supply, and a bit of programming to display video from any source on this cube.
You are going to need 32 x 32 RGB LED panels, LED video wall sender/receiver set, cables, power supply, a computer for configuration, and a few other components to get started. The instructions are available here.