<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2018-07-02</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000716133</issuerCik>
        <issuerName>CINCINNATI BELL INC</issuerName>
        <issuerTradingSymbol>CBB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001206921</rptOwnerCik>
            <rptOwnerName>DODS WALTER A JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>221 EAST FOURTH STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CINCINNATI</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>45202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>On July 2, 2018, pursuant to the Agreement and Plan of Merger, dated July 9, 2017 (the &quot;Merger Agreement&quot;), among the Issuer, Twin Acquisition Corp., a wholly owned subsidiary of the Issuer (&quot;Merger Sub&quot;), and Hawaiian Telcom Holdco, Inc. (&quot;Hawaiian Telcom&quot;), Merger Sub merged with and into Hawaiian Telcom (the &quot;Merger&quot;), with Hawaiian Telcom surviving the Merger as a wholly owned subsidiary of the Issuer. Pursuant to the Merger Agreement and as of the effective time of the Merger, the Reporting Person became a director of the Issuer. This Form 3 presents the beneficial ownership of the Reporting Person at the effective time of the Merger and does not include any securities acquired by the Reporting Person in connection with the closing of the Merger. The Reporting Person will file a Form 4 presenting any acquisition of the Issuer's securities in connection with the closing of the Merger.</remarks>

    <ownerSignature>
        <signatureName>/s/ Christopher J. Wilson by Power of Attorney for Walter A. Dods, Jr.</signatureName>
        <signatureDate>2018-07-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
