You wouldn't multiply by 256 bits in that case, but by 8, I think you mean to say. For 24-bit colour, you'd multiply by 3 bytes. So total bandwidth for 24 bit color is: 1k x 1k x 1k x 60 x 3 = 180 gigabytes per second.
A lot! But there's no reason would couldn't bring that down by orders of magnitude and still have a very commercially useful device.
ie:
512 x 512 x 512 x 10fps x 8bit color(256 grey levels) = 1.25 gigabytes/sec