Multicopters are able to perform high maneuverability yet their potential have not been fully achieved. In this work, we propose a full-body, optimization-based motion planning framework that takes shape and attitude of aerial robot into consideration such that the aggressiveness of drone maneuvering improves significantly in cluttered environment. Our method takes in a series of intersecting polyhedrons that describe a range of 3D free spaces and outputs a time-indexed trajectory in real-time with full-body collision-free guarantee. The drone is modeled as a tilted cuboid, yet we argue that our framework can be freely adjusted to fit multicopters of different shapes. Guaranteeing dynamic feasibility and safety conditions, our framework transforms the original constrained nonlinear programming problem to an unconstrained one in higher dimensions which is further solved by quasi-Newton methods. Benchmark has shown that our method improves the state-of-art with orders of magnitude in terms of computation time and memory usage. Simulations and onboard experiments are carried out as validation.