[tex]\bf \textit{the volume of one small cube is }V=\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\implies V=\cfrac{1}{8}
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\textit{now, the box fits in }128\frac{1}{8}\textit{ of those cubes, thus its volume is}
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128\frac{1}{8}\cdot \cfrac{1}{8}\implies \cfrac{128\cdot 8+1}{8}\cdot \cfrac{1}{8}\implies \cfrac{1025}{8}\cdot \cfrac{1}{8}\implies \cfrac{1025}{64}\implies 16\frac{1}{64}~in^3[/tex]
