Carbon nanotubes (CNTs) are valuable drug carriers since when properly functionalized they transport drugs and anchor directly to cancerous tumors whose more acidic pH causes the drug release. Herein, we study the so-called zigzag and armchair CNTs with haeckelite defects to rank their ability to adsorb doxorubicin (DOX) by determining the DOX-CNT binding free energies using the MM/PBSA and MM/GBSA methods implemented in AMBER. Our results reveal stronger DOX-CNT interactions for encapsulation of the drug inside the nanotube compared to its adsorption onto the defective nanotube external surface. Armchair CNTs with one and two defects exhibit better results compared with those with four and fifteen defects. Each haeckelite defect consists of a pair of square and octagonal rings. DOX-CNT binding free energies are predicted to be dependent on: (i) nanotube chirality and diameter, (ii) the number of defects, (iii) nitrogen doping and (iv) the position of the encapsulated DOX inside the nanotube. Armchair (10,10) nanotubes with two haeckelite defects, doped with nitrogen, exhibit the best drug-nanotube binding free energies compared with zigzag and fully hydrogenated nanotubes and, also previously reported ones with bumpy defects. These results contribute to further understanding drug-nanotube interactions and their potential application to the design of new drug delivery systems.