What Jesus did, Pope Francis said, was to take upon himself "the evil, the filth, the sin of the world, including our own sin," and cleanse it "with his blood, with the mercy and the love of God."
He then recalled how the world is filled with the effects of evil and sin:
"Wars, violence, economic conflicts that hit the weakest, greed for money, power, corruption, divisions, crimes against human life and against creation! And our personal sins: our failures in love and respect towards God, towards our neighbor and towards the whole of creation."
In the face of all this, he asked, "Do we feel weak, inadequate, powerless?"
"But," he responded, "God is not looking for powerful means: it is through the Cross that he has conquered evil! We must not believe the Evil One when he tells us: you can do nothing to counter violence, corruption, injustice, your sins!"
"We must never grow accustomed to evil!" he insisted.
"With Christ," he declared, "we can transform ourselves and the world. We must bear the victory of Christ's Cross to everyone everywhere, we must bear this great love of God."
Pope Francis dedicated his final words to the youth, who were in St. Peter's Square today because Palm Sunday is traditionally the day on which World Youth Day is celebrated at the diocesan level.
"Dear young people," he said, you have "an important part in the celebration of faith! You bring us the joy of faith and you tell us that we must live the faith with a young heart, always, even at the age of seventy or eighty."
"And you are not ashamed of his Cross! On the contrary, you embrace it, because you have understood that it is in giving ourselves that we have true joy and that God has conquered evil through love," he told the youth.
Pope Francis also looked ahead to this coming July, when he will participate in his first World Youth Day as Pope.
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"Dear friends," he said, "I too am setting out on a journey with you, in the footsteps of Blessed John Paul II and Benedict XVI.
"We are already close to the next stage of this great pilgrimage of Christ's Cross. I look forward joyfully to next July in Rio de Janeiro!" he told the young people in St. Peter's Square.
"I will see you in that great city in Brazil! Prepare well – prepare spiritually above all – in your communities, so that our gathering in Rio may be a sign of faith for the whole world."
Following Palm Sunday Mass, Pope Francis spent around 25 minutes moving through the piazza greeting the faithful – an unusually long time for a segment that typically takes about 10 minutes.