This is an effect called “mipmapping”, where a sample is taken of each pixel then overlayed again. This is used to make textures on complex UV layouts to look more even, without being able to see individual pixels.
I don’t believe it is yet possible to turn mipmapping off in Cycles, although I know it was possible in BI…
So basically, i can explain the problem but not really help you…
I guess is a resolution matter. What is the resolution of the image?
Did you subdivide the cube? If the image is low res and the object not subdivided
then the image has to stretch to match the UV.
In edit mode hit A to select all faces of the object then hit W and then select subdivide, do it a couple of times (subdivide)
and increase the resolution of the image, or even better remake it in a High Res Doc this time.
This isn’t a render engine bug, is a texture problem.