The microstructure of partially annealed and additionally rolled 1050 aluminum alloy of commercial purity was monitored using FEG/EBSD in situ heating experiments in order to understand the preferential growth of Cube-oriented grains. A fast reorganization of the deformation sub-structure of Cube and S1{214} <-1-21> grains has been observed by sub-grain growth that consists in a continuous recrystallization mechanism. This occurs as the main recrystallization mechanism at the beginning of the annealing but soon competes with a preferential Cube growth by Strain Induced Boundary Migration (SIBM). An EBSD pattern Image Quality (IQ) analysis attested that Cube grains store less energy than non-Cube oriented grains. TEM observations allowed studying the effect of the additional rolling on the deformation sub-structures depending on the crystallographic orientation. It appears that Cube grains close to the exact orientation contain isolated dislocations and that rotated Cube grains (with 15° spread to the exact orientation) are composed of dislocation cells with thin walls. At the opposite, non-Cube grains are organized in sub-grains with thicker walls and rich in dislocations. Finally, this difference of sub-structure associated to an energy difference between Cube and non-Cube grains explains the preferential Cube growth by SIBM evidenced by the sequence of in situ scans during heating.