What about setting the UV coordinates so that they only encompass the necessary part of the sprite sheet?
So since the sprite sheet is 16x16 blocks, a box is only a small 0.0625 height/width in terms of UV co-ordinates, not pixels.
With that, the top left square would have the following co-ordinates:
X - Y
Top Left: 0.0 - 1.0
Top Right: 0.0625 - 1.0
Bottom Left: 0.0 - 0.9375
Bottom Right: 0.0625 - 0.9375
I believe.