BigQuery Syntax Error: Expected ")" but got keyword CAST at [6:3]

I'm' trying to run the following query in BigQuery but am getting the error from the title. Is there anything I need to adjust in the query below?

INSERT INTO `project_dataset.TABLE_NEW`
(column1, column2, column3, column4, column5, column6, column7, column8, _PARTITIONTIME)
(SELECT
  CAST (column1 AS STRING) column1, 
  CAST (column2 AS STRING) column2,
  CAST (column3 AS STRING) column3,
  CAST (column4 AS INTEGER) column4,
  CAST (column5 AS STRING) column5,
  CAST (column6 AS INTEGER) column6,
  CAST (column7 AS STRING) column7,
  CAST (column8 AS STRING) column8,
  _PARTITIONTIME
FROM `project_dataset.TABLE_OLD`);