14. (12 points) There is a cube $A B C D-E F G H$. The three square faces passing through point $B$ are painted red. Now, cut along some of its edges to get its net. If in the net, the three red squares do not share any common edges, then there are $\qquad$ different ways to cut. (Cuts along the same edges but in different orders are considered the same way.)
【Solution】Solution: According to the analysis, to get a plane development diagram by cutting along the edges of a cube, 7 edges need to be cut. Since after cutting, the three red squares have no common side, then $B A, B F, B C$ need to be cut. Next, we classify whether to cut the three edges $H D, H E, H G$:
(1) Cut 1 edge among $H D, H E, H G$, there are 3 cases;

Assume $H D$ is cut, then 3 more edges need to be cut from $D A, D C, E A, E F, G H, G C$.
Among $D A, D C$, choose one to cut, there are 2 cases;
Among $E A, E F$, choose one to cut, there are 2 cases;
Among $G H, G C$, choose one to cut, there are 2 cases;
There are a total of $3 \times 2 \times 2 \times 2=24$ cases.
(2) Cut 2 edges among $H D, H E, H G$, there are 3 cases, assume $H E, H G$ are cut, then 2 more edges need to be cut from $D A, D C, E A, E F, G H, G C$.

Among $D A, D C$, choose one to cut, there are 2 cases;
Among $E A, E F, G H, G C$, choose one to cut, there are 4 cases;
There are a total of $3 \times 2 \times 4=24$ cases,
(3) Cut 3 edges among $H D, H E, H G$, then 1 more edge needs to be cut from $D A, D C, E A, E F, G H, G C$,

There are a total of 6 cases,
In summary, there are $24+24+6=54$ different cutting methods.