Patients must not be receiving other investigational medications (covered under another IND) within days of study entry or while on study. Actively receiving insulin or requiring fingerstick glucose monitoring at time of ascorbate infusion (unless an exception is granted by the investigational new drug [IND] sponsor, medical monitor, and the principal investigator [PI]) Patients actively receiving insulin are excluded unless approved by the investigational new drug (IND) medical monitor, IND sponsor, and the study principal investigator (PI) Patients requiring daily finger-stick blood glucose measurements unless approved by the IND medical monitor, IND sponsor, and the study PI DONOR: The unmanipulated CB unit(s) will be Food and Drug Administration (FDA) licensed or will be obtained under a separate investigational new drug (IND), such as the National Marrow Donor Program (NMDP) Protocol -CBA conducted under BB IND- or another IND sponsored by () a participating institution or () an investigator at FHCRC or one of the participating institutions Patients must not be receiving other investigational medications (covered under another IND) within days of study entry or while on study. Patients must not be receiving other investigational medications (covered under another IND) within days of study entry or while on study Patients actively receiving insulin are excluded unless approved by the investigational new drug (IND) medical monitor, IND sponsor, and the study principal investigator (PI) Patients requiring daily finger-stick blood glucose measurements unless approved by the IND medical monitor, IND sponsor, and the study PI Actively receiving insulin at time of ascorbate infusion (unless an exception is granted by the Investigational New Drug [IND] sponsor, medical monitor, and the principal investigator [PI]) Patients actively receiving insulin are excluded unless approved by the IND medical monitor, the IND sponsor, and the treating radiation oncologist Patients must not be receiving other investigational medications (covered under another IND) within days of study entry or while on study. Patients must not be receiving other investigational medications (covered under another IND) while on study. Has participated in any Phase Investigational New Drug (IND) study within prior days or expects to do so within the following days