KöMaL 2015 B4734

Some fields (unit cubes) constituting a cubical lattice of edge 2015 units are infected by an unknown disease. The disease will spread if at least $t$ fields in some row parallel to any edge of the cube are infected $(1 \le t \le 2015)$. In that case, every field of that row will become infected in one minute. How many fields need to be infected initially in order to $a)$ make it possible $b)$ be certain that the infection reaches all fields of the cube?