index.html
```html
<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Live Digital Clock</title>
    <style>
        body {
            font-family: Arial, sans-serif;
            display: flex;
            justify-content: center;
            align-items: center;
            height: 100vh;
            margin: 0;
            transition: background-color 0.3s, color 0.3s;
        }

        .clock {
            font-size: 5rem;
        }

        .toggle-theme-btn {
            position: absolute;
            top: 20px;
            right: 20px;
            padding: 10px 20px;
            cursor: pointer;
        }
        
        /* Light theme styles */
        .light-theme {
            background-color: #ffffff;
            color: #000000;
        }

        /* Dark theme styles */
        .dark-theme {
            background-color: #000000;
            color: #ffffff;
        }
    </style>
</head>
<body class="light-theme">
    <div class="clock" id="clock">--:--:--</div>
    <button class="toggle-theme-btn" id="toggleThemeBtn">Toggle Theme</button>
    
    <script>
        function updateClock() {
            const clockElement = document.getElementById('clock');
            const now = new Date();
            const hours = String(now.getHours()).padStart(2, '0');
            const minutes = String(now.getMinutes()).padStart(2, '0');
            const seconds = String(now.getSeconds()).padStart(2, '0');
            clockElement.textContent = `${hours}:${minutes}:${seconds}`;
        }

        function toggleTheme() {
            const body = document.body;
            body.classList.toggle('light-theme');
            body.classList.toggle('dark-theme');
        }

        document.getElementById('toggleThemeBtn').addEventListener('click', toggleTheme);

        updateClock();
        setInterval(updateClock, 1000);
    </script>
</body>
</html>
```