Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:C
['D3 DEG A2 G ABc BAG AGE', 'dBG AGA BGE', 'BDD ADD ABc BAG AGE']  
X:1
L:1/8
M:4/4
K:C
 |[M:6/8][K:Dmix] D3 DEG | A2 G ABc | BAG AGE | GEA GED | D3 DEG | A2 G ABc | BAG AGE | GED D3 :: 
 ded dBG | AGA BGE | ded dBG | ABA GBd | g2 e dBG | AGA BGE | B2 G AGE | GAG GFG :: ADD BDD | 
 ADD ABc | BAG AGE | GEA GED | ADD BDD | ADD ABc | BAG AGE | GED D3 :|  