Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/4
K:F
['cccc cc A2 cc/c/cB/B/']  
X:1
L:1/8
M:2/4
K:F
 F | cccc | cc A2 | cc/c/cB/B/ | AGFF | cccc | cc A2 | cc/c/cB/B/ | AGFd | dccc | Bddd | cAAA | 
 AAcc | BA G2 | GG G2 | cccc | c/c/ F2 |]  