舒欣（Shu Xin）有一个尺寸为 32 cm × 12 cm × 24 cm 的长方体木块。她把这个木块的所有面都涂上了油漆。然后，她将木块切成了边长为 2 cm 的正方体。

1. Find the number of 2-cm cubes along the length, width, and height.

Number of cubes along length = $32 \div 2 = 16$
Number of cubes along width = $12 \div 2 = 6$
Number of cubes along height = $24 \div 2 = 12$

2. Calculate the total number of cubes.

Total number of cubes = $16 \times 6 \times 12 = 1152$

1. Find the number of 2-cm cubes along each dimension of the unpainted inner block

Number of cubes along the length $= (32 \div 2) - 2 = 16 - 2 = 14$
Number of cubes along the width $= (12 \div 2) - 2 = 6 - 2 = 4$
Number of cubes along the height $= (24 \div 2) - 2 = 12 - 2 = 10$

2. Calculate the total number of unpainted cubes

Number of unpainted cubes $= 14 \times 4 \times 10 = 560$