Use pliers to push the wire further in (you don’t want the wires to stick out). Put the palm tree away for a moment - place it f.ex. on crumpled paper towels.

If want the palm tree to go on the cake (instead of being attached to the side of the cake) you will need to insert a wooden skewer (bbq stick) from the bottom of the trunk. Apply some glue on the stick. It should go inside the trunk to at least about 2/3 of the length and stick out so that you can trim it to the depth of the cake later. If the stick reaches the bottom of the cake (board) it will support the tree - it won't sink into the cake and won't lean to the sides. If you are planning to put the palm tree in the cake, the tree trunk needs to be dry (very firm). Remember that the tree can't be very big compared to the size of the cake, otherwise it might rip through the cake.