Export of the matrix in a order?

I want to export the following matrix,

MatrixForm[Flatten /@Table[{f[a, b, c], a, b, c}, {a, 0, 2}, {b, 0, 2}, {c, 0, 2}]]

is there any way to export the first four columns and the next four columns below to the first exported columns?

So the one exported file (.dat or .txt) contains only 4 columns with many rows.

something like,

f[0,0,0] 0 0 0
f[1,0,0] 1 0 0
f[2,0,0] 2 0 0
f[0,0,1] 0 0 1
f[1,0,0] 1 0 1
f[2,0,1] 2 0 1
.
.
.
.
.
.

Export[
 "file.txt",
 Flatten[Transpose[
   Table[{f[a, b, c], a, b, c}, {a, 0, 2}, {b, 0, 2}, {c, 0, 2}], {3, 
    1, 2}], 2],
 "Table"
 ]