Having a strong core is a fundamental part of cycling - It increases your stability and efficiency when on the bike and helps to prevent injury.
Below is a workout I've put together that focusses on strengthening your core. There's no need for weights, as all the exercises are body weight bearing - So you could even carry it out in the front room!
Simply start by doing each exercise for 20 seconds with a 10 second break between each one.
Repeat the programme 3 times.
As strength begins to build increase the length of each exercise by 10 seconds building up to 40 seconds for each one.
Do this programme 1-2 times a week, mixed in with your other strengthening and cardio work, and you'll soon start noticing the benefits!