I need to draw a large set of cubes, all with (possibly) unique textures on each side. Some of the textures also have parts of transparency. The cubes that are behind ones w
XNA (and DirectX and all major 3D libraries) take in consideration something called culling. Although from your code I cannot tell for sure, from the images I think this is your problem. The polygons that you don't see have the vertices in the wrong order. If this is the problem, you have two solutions:
device.RenderState.CullMode = CullMode.None;
if I remember correctly)