How to smooth the blocks of a 3D voxel world?

You should probably have a look at the marching cubes algorithm and work from there. You can easily control the smoothness of the resulting blob:

1. Imagine that each voxel defines a field, with a high density at it's center, slowly fading to nothing as you move away from the center. For example, you could use a function that is 1 inside a voxel and goes to 0 two voxels away. No matter what exact function you choose, make sure that it's only non-zero inside a limited (preferrably small) area.
2. For each point, sum the densities of all fields.
3. Use the marching cubes algorithm on the sum of those fields
4. Use a high resolution mesh for the algorithm

In order to change the look/smoothness you change the density function and the threshold of the marching cubes algorithm. A possible extension to marching cubes to create smoother meshes is the following idea: Imagine that you encounter two points on an edge of a cube, where one point lies inside your volume (above a threshold) and the other outside (under the threshold). In this case many marching cubes algorithms place the boundary exactly at the middle of the edge. One can calculate the exact boundary point - this gets rid of aliasing.

Also I would recommend that you run a mesh simplification algorithm after that. Using marching cubes results in meshes with many unnecessary triangles.

As an alternative to my answer above: You could also use NURBS or any algorithm for subdivision surfaces. Especially the subdivision surfaces algorithms are spezialized to smooth meshes. Depending on the algorithm and it's configuration you will get smoother versions of your original mesh with

• the same volume
• the same surface
• the same silhouette

and so on.