Question

Is the calculation of percentage of each atom within a Body centered cubic cell AKA volume of the BCC cell same as the atomic packing factor for the BCC unit cell.

The BCC % is 68%. the atomic packing factor is just 0.68. Am I completely wrong?

And also how do i calculate the lattice constant given Fe is the atom and it's radius is 0.124nm.
I know the lattice constant is a, b, c

would a, b,c be all the same because it's a cube?
No. The bcc is 68% and the factor is, of course, 0.68.
Fe is a bcc, also, and if you know r, then 4r = a(3)<sup>2</sup> and you can calculate a.
Here is a site that gives a,b,c and much more information about iron. a, b, and c are about 286 something pm. The volume would, of course, be a<sup>3</sup> for the unit cell.
4r = a(3)<sup>1/2</sup>

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