There is no ability to look at log files for the cluster. They are only available per cluster instance.
# List Log Files
aws rds describe-db-log-files --db-instance-identifier ${INSTANCE_ID}
# Note: if you do no specify --output text you will get the log in a JSON format
ERROR_LOG="error/mysql-error-running.log" # For MySQL variant
ERROR_LOG="error/postgres.log" # PostgreSQL
aws rds download-db-log-file-portion --db-instance-identifier ${INSTANCE_ID} --log-file-name ${ERROR_LOG} --output text
$ aws rds describe-db-log-files --db-instance-identifier ${INSTANCE_ID}
{
"DescribeDBLogFiles": [
{
"LastWritten": 1639516200000,
"LogFileName": "error/mysql-error-running.log",
"Size": 105234
},
{
"LastWritten": 1639513801000,
"LogFileName": "error/mysql-error-running.log.2021-12-14.20",
"Size": 1407077
},
{
"LastWritten": 1639514400000,
"LogFileName": "error/mysql-error-running.log.2021-12-14.21",
"Size": 13452
},
{
"LastWritten": 1639517082000,
"LogFileName": "error/mysql-error.log",
"Size": 19071
},
{
"LastWritten": 1639516200000,
"LogFileName": "external/mysql-external.log",
"Size": 1633
}
]
}
{
"DescribeDBLogFiles": [
{
"LastWritten": 1668544339598,
"LogFileName": "error/postgres.log",
"Size": 1635
},
{
"LastWritten": 1668544339602,
"LogFileName": "error/postgresql.log.2022-11-15-2024",
"Size": 8756
},
{
"LastWritten": 1668548605075,
"LogFileName": "error/postgresql.log.2022-11-15-2100",
"Size": 1958
},
{
"LastWritten": 1668549600175,
"LogFileName": "error/postgresql.log.2022-11-15-2200",
"Size": 0
}
]
}