imc

We can use Euler's polyhedron formula that says that $F+V=E+2$. We know that there are originally $6$ faces on the cube, and each corner cube creates $3$ more. $6+8(3)=30$. In addition, each cube creates $7$ new vertices while taking away the original $8$, yielding $8(7)=56$ vertices. Thus $E+2=56+30$, so $E=\boxed{84}$