A plane passes through three vertices of a cube and divides the cube into two parts, a green part and a blue part, and they remain together, as shown below. Eight such cubes are assembled to create a larger cube, where blue portion is on the inside as shown on the right. Calculate the volume of blue part in the larger cube, if the edge of the original cube is 1 cm.
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A plane cutting through three adjacent vertices of a unit cube always cuts off a tetrahedron of volume $\frac{1}{6}\text{ units}^3$. Combining 8 such tetrahedra at a single point forms a regular octahedron of volume $\frac{4}{3}\text{ units}^3$.
Step 1: Volume of one corner tetrahedron. Cutting a cube through three adjacent vertices removes a tetrahedron of volume $\tfrac{1}{6}\times1^3=\tfrac{1}{6}$ cm$^3$. Step 2: Eight cubes. The $2\times2\times2$ assembly holds 8 blue tetrahedra: $8\times\tfrac{1}{6}=\tfrac{4}{3}$. \[ \boxed{\tfrac{4}{3}\approx1.33 \text{ cm}^3} \]
