I suggest:

1) be sure to pad the month and day values so that the final format is a full yyyymmdd.

2) apply column names to make the code easier to understand and maintain

3) use CAST() as it will always accept 'yyyymmdd' with no conversion code required.

SELECT CAST(Field1_year + Field1_month + Field1_day AS datetime)

FROM ( --dbo.tablename

SELECT '160416' AS Field1

) AS a1

CROSS APPLY (

SELECT

'20' + LEFT(a1.Field1,2) AS Field1_year,

RIGHT('0' + SUBSTRING(a1.Field1,3,2), 2) AS Field1_month,

RIGHT('0' + SUBSTRING(a1.Field1,5,2), 2) AS Field1_day

) AS ca1