I have a lattice of large spheres:
vecs = Entity["Lattice", "BodyCenteredCubic"]["MinimalVectors"];
bcc = Append[vecs, {0, 0, 0}];
Graphics3D[{Opacity[.6], Ball[#, Sqrt[3]/2] & /@ bcc}]
I would like to fill in the transparent space between the spheres with some semi-transparent color instead of it simply being empty space between the spheres. Is this possible?

