Cnut sailed to Denmark for his coronation. A letter he wrote at the time states that he also intended to end Danish incursions into England for plunder. This did not sit well with some Danes, who found England ripe for plucking in the past, but now their king forbade them. After seeing to affairs in Denmark, Cnut left his sister Estrid's husband, Ulf Thorgilsson, as regent. Cnut had a son by Queen Emma, Harthacnut, whom he left with Estrid and Ulf to raise. Cnut was back in England in 1020.
Because of his time in England, the King of Norway, Olaf II Haraldsson, decided Denmark was open to attacks. Olaf in 1016 had become king of Norway after capturing it from Denmark in the Battle of Nesjar. (Norway was half-ruled by Denmark and Sweden, but the person managing the Danish part joined Cnut on his attack on England, leaving an opening for Olaf.) Cnut decided he needed a show of Danish strength in the North Sea, so he mounted a successful expedition against Jomsborg (location unknown to modern scholars), the stronghold of the Jomsvikings.
In Denmark, his regent Ulf declared that the child Harthacnut was king (being resident in Denmark and not far away in England like Cnut pleased the locals), and that Ulf was now Harthacnut's regent, not Cnut's. Learning this, Cnut sailed to Denmark to set things straight. A battle in 1026 against the Norwegians and Swedes to firmly establish who was in charge was successful. Ulf fought alongside Cnut, but this was not sufficient for Cnut to be assured of his loyalty. One day the two were playing chess and started arguing. The next day, Christmas Day 1026, Ulf was killed by one of Cnut's nobles, apparently with Cnut's blessing.
King of England and Denmark, but he had one more to go to establish what is refereed to as the North Sea Empire. He set his sights on Norway (and maybe a little Sweden?). I'll explain tomorrow.