Using Monte Carlo simulations, we explore the magnetic phase diagram of triangular spin tubes coupled with a ferromagnetic intertube interaction for CsCrF₄. The planar structure of the coupled tubes is topologically equivalent to the kagome-triangular lattice, which induces nontrivial frustration effects in the system. We particularly find that, depending on the intertube coupling, various ordered phases are actually realized, such as incommensurate order, ferromagnetic order, and cuboc order, which is characterized by the noncoplanar spin structure of the 12 sublattices accompanying the spin chirality breaking. We also discuss the relevance of the results to recent experiments on CsCrF₄. <P />...