First of all, we must know under what circumstances Muslims are allowed to fight non-Muslims.
Verses specify the boundaries that justify a war when transgressed by non-muslims:
“God does not forbid you from being kind and equitable to those who do not fight you because of religion and do not expel you from your homes. Indeed, God likes those who are equitable.
God only forbids you from making friends of those who fight you because of religion or expel you from your homes or aid in your expulsion. The ones that make friends of them are the wrongdoers.“ (Al-Mumtahanah/The Examined One 60:8-9)
According to the verse, the following are reasons for starting a war against non-Muslims:
1. Non-Muslims starting a battle against Muslims due to their religion
2. Driving Muslims out of their homes
3. Supporting the ones driving Muslims out
We cannot make friends with or exhibit sympathy to the ones that cross these lines. If non-Muslims transgress any of these three, Muslims have the right to start a war against non-Muslims. Otherwise, Muslims cannot be the side who starts the war, but they always have the right to defend themselves. You can find further detail on this issue on the following link:
Now let us consider the first verse mentioned in your question. To understand al-Enfal 8:61 correctly, we need to read it in its context, from the verse 55 onwards:
إِنَّ شَرَّ الدَّوَابِّ عِنْدَ اللَّهِ الَّذِينَ كَفَرُوا فَهُمْ لَا يُؤْمِنُونَ. الَّذِينَ عَاهَدْتَ مِنْهُمْ ثُمَّ يَنْقُضُونَ عَهْدَهُمْ فِي كُلِّ مَرَّةٍ وَهُمْ لَا يَتَّقُونَ. فَإِمَّا تَثْقَفَنَّهُمْ فِي الْحَرْبِ فَشَرِّدْ بِهِمْ مَنْ خَلْفَهُمْ لَعَلَّهُمْ يَذَّكَّرُونَ. وَإِمَّا تَخَافَنَّ مِنْ قَوْمٍ خِيَانَةً فَانْبِذْ إِلَيْهِمْ عَلَى سَوَاءٍ إِنَّ اللَّهَ لَا يُحِبُّ الْخَائِنِينَ. وَلَا يَحْسَبَنَّ الَّذِينَ كَفَرُوا سَبَقُوا إِنَّهُمْ لَا يُعْجِزُونَ. وَأَعِدُّوا لَهُمْ مَا اسْتَطَعْتُمْ مِنْ قُوَّةٍ وَمِنْ رِبَاطِ الْخَيْلِ تُرْهِبُونَ بِهِ عَدُوَّ اللَّهِ وَعَدُوَّكُمْ وَآَخَرِينَ مِنْ دُونِهِمْ لَا تَعْلَمُونَهُمُ اللَّهُ يَعْلَمُهُمْ وَمَا تُنْفِقُوا مِنْ شَيْءٍ فِي سَبِيلِ اللَّهِ يُوَفَّ إِلَيْكُمْ وَأَنْتُمْ لَا تُظْلَمُونَ. وَإِنْ جَنَحُوا لِلسَّلْمِ فَاجْنَحْ لَهَا وَتَوَكَّلْ عَلَى اللَّهِ إِنَّهُ هُوَ السَّمِيعُ الْعَلِيمُ
“The worst creatures in the sight of God are those who ignore Him. This is because they do not believe and trust. Whenever you (Prophet) make a treaty with them, they break it, for they are not mindful of God. If you confront them in battle, disperse them (in such a way) that those who are behind them also disperse. So that they may take admonition. If you have reason to fear treachery from a group of people (with whom you had made a treaty), tell them that you repeal the treaty under equal terms (in return for what they do). Verily, God does not love the treacherous! Those ignorers should not think that they can run away and escape. They cannot incapacitate you. Prepare whatever forces you (believers) can muster, including warhorses, to frighten off God’s enemies and yours, and warn others unknown to you but known to God. Whatever you give in God’s cause will be repaid to you in full, and you will not be wronged. If they incline to peace, you too incline to peace, and rely on God. He listens to all and knows all.” (al-Anfal 8:55-61)
As you can see, this verse is about a group of people who are prepared to violate the treaty they made with Muslims. In this case, Muslims have the right to terminate the treaty. When that group learns of the termination of treaty, they may change their minds and incline to peace. Of course, to be able to incline to peace they will in the least have to comply with the first treaty they had made, and/or Muslims may demand the fulfillment of additional conditions. If the necessary conditions are met, Muslims should also incline to peace. This is logical, because the aim of war is not shedding blood but protecting the rights of believers as well as innocent people. Note that, God commands gathering the warhorses and other forces in order to frighten off the enemy. If the ignorers are frightened by the prepared forces, regret their treachery, turn around from their mistakes and seek peace, Muslims are then advised to incline to peace.
The second verse you mention is:
إِنَّ الَّذِينَ كَفَرُوا وَصَدُّوا عَنْ سَبِيلِ اللَّهِ ثُمَّ مَاتُوا وَهُمْ كُفَّارٌ فَلَنْ يَغْفِرَ اللَّهُ لَهُمْ. فَلَا تَهِنُوا وَتَدْعُوا إِلَى السَّلْمِ وَأَنْتُمُ الْأَعْلَوْنَ وَاللَّهُ مَعَكُمْ وَلَنْ يَتِرَكُمْ أَعْمَالَكُمْ
“Those who disbelieve and obstruct God’s path, and oppose the Messenger when they have been shown guidance, do not harm God in any way. He will make their deeds go to waste. Oh you who believe and trust in God! Obey God and obey the Messenger. Do not cause your actions to become of no worth. Those who ignore (God’s verses) and obstruct the Way of God, and then die as ignorers, God will not forgive them. (Since you are believers) you are superior and God is with you. Then, do not lose heart and call for peace. He never leaves you alone in your deeds.” (Muhammad 47:32-35)
The second set of parenthesis “since you are believers” has been added because of the following verse, which explains the reason of the superiority of Muslims. Superiority is not granted by birth but granted if they duly trust in God according to the verse below:
وَلَا تَهِنُوا وَلَا تَحْزَنُوا وَأَنْتُمُ الْأَعْلَوْنَ إِنْ كُنْتُمْ مُؤْمِنِينَ. إِنْ يَمْسَسْكُمْ قَرْحٌ فَقَدْ مَسَّ الْقَوْمَ قَرْحٌ مِثْلُهُ وَتِلْكَ الْأَيَّامُ نُدَاوِلُهَا بَيْنَ النَّاسِ وَلِيَعْلَمَ اللَّهُ الَّذِينَ آَمَنُوا وَيَتَّخِذَ مِنْكُمْ شُهَدَاءَ وَاللَّهُ لَا يُحِبُّ الظَّالِمِينَ
“Do not lose heart and do not grieve! If you trust in God (do know that) you are the superior. If you have received a wound, (do know that) those people had received a similar wound too. We circulate such days between people. This is for God to know those who trust in Him and to adopt some of you as witnesses from among you. God does not like the wrongdoers.” (Al-e Imran 3:139-140)
That means, the army of Muslims who duly trust in God would overcome the group of ignorers (kafir) because God is with them. When God is with a group of people, nobody can overcome them. Then, they must take courage from God’s these words, trust in Him and fight against the ignorers. Calling for peace in a case where God is with you would be mistrusting God. This is why calling for peace against the ignorers who obstruct God’s path is forbidden in the verse 47:32-35. Notice that there is no mention of a previous treaty here.