How call DoPopup in runtime cxPopupEdit1.Properties.PopupControl
The DoPopup procedure is a protected procedure of drop-down editors. So, you need to create an accessor for the editor's class to work with its protected methods and properties. See the A1030: How to access a protected class member Knowledge Base article for more information.
If you wish to show the drop-down window of the TcxPopupEdit component, enable the TcxPopupEdit.DroppedDown property:
<AcxPopupEdit>.DroppedDown := True;