You might need an input style for CONVERT:
;WITH Sampledata AS (
SELECT lastrundate = CAST(20130620 AS INT)
)
SELECT
lastrundate_INT = lastrundate,
lastrundate_CHAR8 = CAST(lastrundate AS CHAR(8)),
lastrundate_DATE = CONVERT(DATE, CAST(lastrundate AS CHAR(8)),112)
FROM Sampledata
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden