Remarks on the Pocklington and Padr??-S??ez cube root algorithm in Fq

A cube root algorithm in F_q proposed by Pocklington and later rediscovered by Padró and Sáez is clarified and generalised. Some errors in the result of Padró and Sáez are corrected and a full generalisation of their result is given. A comparison of the implementation of the proposed algorithm with the two most popular cube root algorithms is also given, namely the Adleman-Manders-Miller algorithm and the Cipolla-Lehmer algorithm. To the authors´ knowledge, this comparison is the first one which compares three fundamental algorithms together.