= Solution
A site in a <primitive cubic lattice> has six nearest neighbours, at $\pm a\hat{\mathbf x}$, $\pm a\hat{\mathbf y}$ and $\pm a\hat{\mathbf z}$. Repeating the <Bloch state> calculation with equal <hopping integrals> $t$ along all six bonds gives
$$
\boxed{E(\mathbf k)=E_0+2t[\cos(k_xa)+\cos(k_ya)+\cos(k_za)].}
$$
The cosine sum ranges from $-3$ to $3$ within the first <Brillouin zone>. Therefore
$$
E_{\min}=E_0-6|t|,\qquad E_{\max}=E_0+6|t|,\qquad
\boxed{W=E_{\max}-E_{\min}=12|t|.}
$$
For $t<0$ the minimum is at the zone centre; for $t>0$ the maximum is there.
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