Prior to treatment, patients will have physical and neurologic exams, MRI to measure the extent of tumor, tumor biopsy, and screening laboratory tests. On Day 1, one or two catheters will be inserted directly into the tumor, after which a CT scan will be used to confirm placement. Each patient will receive one IL13-PE38QQR infusion, and the tumor will be surgically removed on approximately Day 15. In the first group of patients, IL13-PE38QQR will be infused directly into the tumor for 4 days. Depending on effectiveness or side effects of the study drug, the duration will be increased stepwise to a maximum of 7 days in subsequent groups of patients. Once duration of infusion has been determined, the dose of IL13-PE38QQR will be increased stepwise (in separate groups of patients), depending on effectiveness or side effects of the study drug. The activity of the drug against the tumor cells will be judged by examining the removed tumor tissue. Patients will have neurologic exams and MRI scans immediately after the resection and every eight weeks until disease progression is observed.