Twitter is a microblogging website that has been useful as a source for human social behavioral analysis, such as political sentiment analysis, user influence, and spread of news. In this paper, we discuss a text cube approach to studying different kinds of human, social and cultural behavior (HSCB) embedded in the Twitter stream. Text cube is a new way to organize data (e.g., Twitter text) in multiple dimensions and multiple hierarchies for efficient information query and visualization. With the HSCB measures defined in a cube, users are able to view statistical reports and perform online analytical processing. Along with viewing and analyzing Twitter text using cubes and charts, we have also added the capability to display the contents of the cube on a heat map. The degree of opacity is directly proportional to the value of the behavioral, social or cultural measure. This kind of map allows the analyst to focus attention on hotspots of concern in a region of interest. In addition, the text cube architecture supports the development of data mining models using the data taken from cubes. We provide several case studies to illustrate the text cube approach, including public sentiment in a U.S. city and political sentiment in the Arab Spring.