drawEvenBlockSphere[r_] :=
 Graphics3D[
  Cuboid[{#[[1]] - Sign[#[[1]]]/2, #[[2]] - Sign[#1[[2]]]/2, #[[3]] -
       Sign[#[[3]]]/2}] & /@
   Select[
    Flatten[Outer[(#1*#2) &,
      Flatten[Array[List, {r + 1, r + 1, r + 1}], 2],
      Flatten[
       Table[{i, j, k}, {i, {1, -1}}, {j, {1, -1}}, {k, {1, -1}}], 2],
       1], 1],
    If[r < 3, (Sqrt[#[[1]]^2 + #[[2]]^2 + #[[3]]^2] < r) &,
     (Sqrt[#[[1]]^2 + #[[2]]^2 + #[[3]]^2] < r &&
        Sqrt[#[[1]]^2 + #[[2]]^2 + #[[3]]^2] > (r - 2)) &]
    ]
  ]