3. (10 points) Cut the large triangular cardboard on the left 3 times to get 4 smaller triangular cardboard pieces of the same size (first operation), see the middle figure, then cut each of the smaller triangular cardboard pieces 3 times to get 16 even smaller triangular cardboard pieces of the same size (second operation), see the right figure. Continue this process, the total number of cuts after the first six operations is $\qquad$.
【Analysis】First, analyze that the second piece is cut 3 times, becoming 4 pieces, and then each piece is cut 3 times, continuing the calculation.

【Solution】Solution: According to the problem:
The first time is cutting 3 times to become 4 pieces.
The second time is cutting each piece 3 times, totaling 12 cuts to become 16 pieces.
The third time is $16 \times 3=48$ (cuts); the number of pieces is $16 \times 4=64$ (pieces);
The fourth time is $64 \times 3=192$ (cuts); the number of pieces is $64 \times 4=256$ (pieces);
The fifth time is $256 \times 3=768$ (cuts); the number of pieces is $256 \times 4=1024$ (pieces);
The sixth time is $1024 \times 3=3072$ (cuts).
$$
3+12+48+192+768+3072=4095 \text {. }
$$

Therefore, the answer is: 4095