We demonstrate a simple but efficient design for forming tunable single, double and triple quantum dots (QDs) in a sub-μm-long carbon nanotube (CNT) with two major features that distinguish this design from that of traditional CNT QDs: the use of i) Al2Ox tunnelling barriers between the CNT and metal contacts and ii) local side gates for controlling both the height of the potential barrier and the electron-confining potential profile to define multiple QDs. In a serial triple QD, in particular, we find that a stable molecular coupling state exists between two distant outer QDs. This state manifests in anti-crossing charging lines that correspond to electron and hole triple points for the outer QDs. The observed results are also reproduced in calculations based on a capacitive interaction model with reasonable configurations of electrons in the QDs. Our design using artificial tunnel contacts and local side gates provides a simple means of creating multiple QDs in CNTs for future quantum-engineering applications.