Ice King create Princess Bubblegum but due to a accident lose his memories, the princess devastated leave the Ice King to seek a cure in the land of Ooo. In order to increase her chance of success she attempt to clone her body with disastrous result, in the end she perfect the recipe to create the first candy people. In time her search for a cure lead her to a similar disaster(reattempting to clone her body is a success but transferring her memories fail) end in failure, having lost her memories of the Ice King she establish the Candy Kingdom.
Season 4 episode 9 "Princess Monster Wife" How did the Ice King manage to create a princess out of princess parts?
Season 5 episode 14 "Simon & Marcy" During the episode you see what resemble a pink bubblegum stretch across a bridge, and during the end a miniature bubblegum that seem to be alive sticking on Simon suit.
Season 5 episode 31 "Too Old" During the episode you see that Princess Bubblegum is capable of erasing memories.
Season 5 episode 34 "The Vault" During the episode it show Princess Bubblegum in the process of establishing the Candy Kingdom.