6. If the length, width, and height of a rectangular prism are all natural numbers, and the sum of all its edge lengths equals its volume, then it is called a "perfect rectangular prism". The maximum volume of a "perfect rectangular prism" is $\qquad$ .
Let the length, width, and height of a "perfect rectangular prism" be $a, b, c$, and assume $a \geqslant b \geqslant c$. Thus, $a b c = 4(a + b + c) \leqslant 12 a \Rightarrow b c \leqslant 12 \Rightarrow c \leqslant 3$.
If $c = 1$, then $a b = 4(a + b + 1) \Rightarrow (a - 4)(b - 4) = 20 \Rightarrow a b c \leqslant 120$; if $c = 2$, then $a b = 2(a + b + 2) \Rightarrow (a - 2)(b - 2) = 8 \Rightarrow a b c \leqslant 60$; if $c = 3$, then $3 a b = 4(a + b + 3) \Rightarrow (3 a - 4)(3 b - 4) = 52 \Rightarrow a b c = 60$. In summary, the maximum volume of a "perfect rectangular prism" is 120.