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Cutting a $n$-dimensional cubic cake

Given a cubic cake, defined as $\{(x,y,z)|0\leq x,y,z\leq 1\}$. We cut it by the planes $p_1\leftrightarrow x=y$ $p_2\leftrightarrow y=z$ $p_3\leftrightarrow x=z$. How many pieces will we have ...