My son is a personal trainer.
Years ago, when I first became more serious about cycling, I wanted to begin an off-season training program. I asked my son, “if you could only do one strength exercise to improve on the bike, what would you recommend?”.
Without hesitation, he said “Lunges!”
It makes sense. Cycling is a one legged sport. So are lunges. They focus on the quads and buttocks. The key cycling muscle group.
I began doing a lot of lunges, and other exercises.
Now, years later, if someone asked me the same question, I’d say –
“I would have to recommend 2 exercises. The squat lightly loaded with a single dumbbell held in front of your chest, and a straight arm plank.”
These exercises target the cycling muscles – quads, flutes, core – best.
If I only have time for 2 exercises, I do these, and I do them most days through the year. Some days, I may just do a few reps. Other days, I’ll do a lot.
PedalWORKS 
I’ve been training for triathlon and endurance activities for several years now with a personal trainer. He makes me do the most ludicrous and cry-inducing lunges, squats, and deadlifts there are. Where he comes up with some of his ideas for those basic exercises, I will never know. I’m not fast. That would come from a different kind of training. But I have to admit my legs and glutes are pretty darned strong.
They know how to make it hard to test your metal don’t they. I’ve never been brought to tears, yet š