The double-cone ignition (DCI) scheme has been proposed as one of the alternative approaches to inertial confinement fusion, based on direct-drive and fast-ignition, in order to reduce the requirement for the driver energy. To evaluate the conical implosion energetics from the laser beams to the plasma flows, a series of experiments have been systematically conducted. The results indicate that 89%-96% of the laser energy was absorbed by the target, with moderate stimulated Raman scatterings. Here 2%-6% of the laser energy was coupled into the plasma jets ejected from the cone tips, which was mainly restricted by the mass reductions during the implosions inside the cones. The supersonic dense jets with a Mach number of 4 were obtained, which is favorable for forming a high-density, nondegenerated plasma core after the head-on collisions. These findings show encouraging results in terms of energy transport of the conical implosions in the DCI scheme.