In this paper, we present a 3D pose regression model using Convolutional Neural Networks (CNNs) for unconstrained end-to-end fetal brain pose estimation in fetal MRI. We focus on investigating across different pose representation schemes and address the problem of ambiguous rotation labels by introducing the rotation matrix formalism for our ground truth data. We propose a continuous 6D rotation matrix representation for efficient and robust direct pose regression. Our model learns to predict different rotation representations of the 3D pose directly based on the MRI volume. We used a geodesic loss to evaluate our model and compare its performance with alternative methods. We trained and tested our model on arbitrarily oriented MRI volumes of fetal brains scanned in-utero at a wide gestational age range. Experimental results on synthetically transformed data, show that our method with a continuous 6D rotation matrix representation, achieved an average geodesic error of 6.33 • without any post-processing, which was smaller than the error for all competing methods. Our proposed method can be a useful base for fetal brain motion tracking, motion detection, and 3D reconstruction. Code, data, and the trained models are available at https://github.com/bchimagine/fetal-brain-pose-estimation.