= Solution
For $|k_i a|\ll1$, expand each cosine to second order:
$$
E(\mathbf k)=E_0+6t-ta^2(k_x^2+k_y^2+k_z^2)+O(ta^4k^4).
$$
To this order a fixed energy fixes $k_x^2+k_y^2+k_z^2$, so the constant-energy surfaces are <spheres>. The <band effective mass> tensor satisfies
$$
(m^{*-1})_{ij}=\frac1{\hbar^2}\frac{\partial^2E}{\partial k_i\partial k_j}
=-\frac{2ta^2}{\hbar^2}\delta_{ij},\qquad
\boxed{m^*=-\frac{\hbar^2}{2ta^2}.}
$$
For bonding hopping $t<0$ this is a positive electron mass at the band bottom. If $t>0$, $k=0$ is a maximum with negative electronic mass, or positive <electron hole> mass $\hbar^2/(2ta^2)$. The spherical shape is a quadratic approximation; cubic anisotropy appears in the fourth-order terms.
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